Biomedicalengineering

2008-02-10T00:39:00.000+03:30

Neocortical Dynamics: Implications for
Understanding the Role of Neurofeedback and
Related Techniques for the Enhancement of AttentionJoel F. Lubar1
For nearly 25 years, EEG biofeedback (neurofeedback) has been utilized in research and
clinical settings for the treatment and investigation of a number of disorders ranging from
attention deficit hyperactivity disorder to seizure disorders as well as many other established
and investigational applications. Until recently, mechanisms underlying the generation and
origins of EEG have been poorfy understood but now are beginning to become much man;
clarified Now it is important to combine the information gathered on the genesis of EEG
and neocortical dynamics with the findings from neurofeedback investigations. This will help
us to develop models of how neurofeedback might operate in producing the changes in EEG
and in clinical symptomatology. We know that the cortex operates in terms of resonant loops
between neocortical columns of cells known as local, regional, and global resonances. These
resonances determine the specific EEG frequencies and are often activated by groups of cells
in the thalamus known as pacemakers. There are complex excitatory and inhibitory
interactions within the cortex and between the cortex and the thalamus that allow these loops
to operate and provide the basis for learning. Neurofeedback is a technique for modifying
these resonant loops, and hence, modifying the neurophysiological and neurological basis for
learning and for the management of a number of neurologically based disorders. This paper
provides an introduction to understanding EEC and neocortical dynamics and how these
concepts can be used to explain the results of neurofeedback training and other interventions
particularly in the context of understanding attentive mechanisms and for the management
of attention deficit/hyperactivity disorders.
KEY WORDS: words: neocortical dynamics; neurofeedback; attention; ADHD; ADD.

2008-02-10T00:36:00.000+03:30

An Event-Related fMRI Study of
Visual and Auditory Oddball Tasks
Kent A. Kiehl1, Kristin R. Laurens2, Timothy L. Duty3,
Bruce B. Forster4, and Peter F. Liddle5
1Institute of Living, Department of Psychiatry, Yale University School of Medicine
Departments of 2Psychiatry, 3Physics, and 4Radiology, University of British Columbia
5Department of Psychiatry, University of Nottingham
Accepted for publication: 12 May 2001
Keywords: Event-related fMRI, oddball, P300, P3, novel, target, visual stimuli
Journal of Psychophysiology 15 (2001) 221–240 © 2001 Federation of European Psychophysiology Societies
Abstract Whole brain event-related functional magnetic resonance imaging (fMRI) techniques were employed to elucidate the
cerebral sites involved in processing rare target and novel visual stimuli during an oddball discrimination task. The analyses of the
hemodynamic response to the visual target stimuli revealed a distributed network of neural sources in anterior and posterior cingulate,
inferior and middle frontal gyrus, bilateral parietal lobules, anterior superior temporal gyrus, amygdala, and thalamus. The analyses
of the hemodynamic response for the visual novel stimuli revealed an extensive network of neural activations in occipital lobes and
posterior temporal lobes, bilateral parietal lobules, and lateral frontal cortex. The hemodynamic response associated with processing
target and novel stimuli in the visual modalitywere also comparedwith data froman analogous study in the auditory modality (Kiehl
et al., 2001). Similar patterns of activation were observed for target and novel stimuli in both modalities, but there were some
significant differences. The results support the hypothesis that target detection and novelty processing are associated with neural
activation in widespread neural areas, suggesting that the brain seems to adopt a strategy of activating many potentially useful brain
regions despite the low probability that these brain regions are necessary for task performance.

2008-02-10T00:35:00.000+03:30

EEG biofeedback: physiological behavior modification.
Sterman MB.
The author reviews the use of operant conditioning to alter electroencephalogram (EEG) patterns. A discrete rhythmic EEG pattern directly related to modulation of motor patterns (sensorimotor rhythm, SMR) was brought under voluntary control in the cat. This technique was modified for use in epileptic human volunteers in order to reduce motor seizures. The use of a newer experimental design and its successful application in one subject is described.

PMID: 7301228 [PubMed - indexed for MEDLINE]

www.pubmed.com

2008-02-10T00:34:00.001+03:30

Brain-computer communication: self-regulation of slow cortical potentials for verbal communication.
Kübler A, Neumann N, Kaiser J, Kotchoubey B, Hinterberger T, Birbaumer NP.
Institute of Medical Psychology and Behavioral Neurobiology, University of Tübingen, Tübingen, Germany. andrea.kuebler@uni-tuebingen.de

OBJECTIVE: To test a training procedure designed to enable severely paralyzed patients to communicate by means of self-regulation of slow cortical potentials. DESIGN: Application of the Thought Translation Device to evaluate the procedure in patients with late-stage amyotrophic lateral sclerosis (ALS). SETTING: Training sessions in the patients' homes. PARTICIPANTS: Two male patients with late-stage ALS. INTERVENTIONS: Patients learned voluntary control of their slow cortical potentials by means of an interface between the brain and a computer. Training was based on visual feedback of slow cortical potentials shifts and operant learning principles. The learning process was divided into small steps of increasing difficulty. MAIN OUTCOME MEASURES: Accuracy of self-control of slow cortical potentials (percentage of correct responses). Learning progress calculated as a function of training session. RESULTS: Within 3 to 8 weeks, both patients learned to self-regulate their slow cortical potentials and to use this skill to select letters or words in the Language Support Program. CONCLUSIONS: This training schedule is the first to enable severely paralyzed patients to communicate without any voluntary muscle control by using self-regulation of an electroencephalogram potential only. The protocol could be a model for training patients in other brain-computer interface techniques. Copyright 2001 by the American Congress of Rehabilitation Medicine and the American Academy of Physical Medicine and Rehabilitation.

www.pubmed.com

2008-02-10T00:33:00.001+03:30

Mathematical model of a learning process by biofeedback

[Article in French]

Gallego J, Laurenti-Lions L.

The aim of Biofeedback is to teach a subject to control some of his biological functions. This experimental method was numerous therapeutic applications. General laws of these particular learning processes have not yet been well understood. Mathematical models can be used in order to make evident these laws can lead to an optimization of the learning processes. The stochastic model presented here underlines the shortcomings of certain experimental procedures. Although it has been performed from one of our particular experiments, it can be applied to analogous experiments.

www.pubmed.com

2008-02-10T00:31:00.000+03:30

A MATHEMATICAL MODEL OF BIOFEEDBACK
AND ITS RELATION TO NEURAL ACTIVITY
C. Nishimura*, L-Q. Wang**, A. Nagase*, K. Terada* and Y. Miyamoto***
*Toho University School of Medicine, Tokyo, Japan
**Research Center for Advanced Technologies, Tokyo Denki University, Tokyo, Japan
***Department of Mechanical Engineering, Osaka Sangyo University, Osaka, Japan
nishimuc@med.toho-u.ac.jp
Abstract: Biofeedback is an acquisition technique of self-regulation ability of a biological function, of which we are normally unaware, through a series of training aided by an additional outer feedback pathway. We proposed a mathematical model of biofeedback in which a learning system on the conscious level learns characteristics of a subconscious regulation system corresponding to the biological function. When the learning converges, the learning system itself becomes an inverse system of the regulation system. Then, if a regulation command is put to the learning system on the conscious level, it drives the regulation system strictly following the command without the outer feedback pathway, which enables voluntary control of the biological function. Based on the model, we measured neural activities relating to a phenomenon of state alteration of consciousness in the course of training in search for an appropriate connection between the learning system and the target regulation system. The situation was modelled as an interpretational change in depth of an ambiguous stereogram. Functional MRI measurement revealed neural activities in bilateral prefrontal area. The results show an important role of neural activities in the prefrontal area in connecting the learning system with the appropriate subconscious regulation system.

2008-02-10T00:29:00.000+03:30

A learning model of autonomic function
in biofeedback
Chiaki Nishimura a,⁎, Li-Qun Wang b, Aki Nagase a,
Kazuko Terada a, Yoshifumi Miyamoto c,
Hisayuki Tsukuma a, Masuo Muro a
a Toho University School of Medicine, Japan
b Research Center for Advanced Technologies, Tokyo Denki University, Japan
c Department of Mechanical Engineering, Osaka Sangyo University, Japan
Abstract. Biofeedback is an acquisition technique of self-regulation ability of an autonomic
function, of which we are normally unaware, through a series of training aided by an additional outer
feedback pathway. We proposed a mathematical model of biofeedback in which a learning system on
the conscious level learns characteristics of a subconscious regulation system corresponding to the
biological function. When the learning converges, the learning system itself becomes an inverse
system of the regulation system. Then, if a regulation command is put to the learning system on the
conscious level, it drives the regulation system strictly following the command without the outer
feedback pathway, which enables voluntary control of the biological function. © 2007 Elsevier B.V.
All rights reserved.
Keywords: Biofeedback; Learning; Mathematical model; Autonomic function; Self-regulation

www.elsevier.com

2008-02-03T22:35:00.000+03:30

learning model of autonomic function
in biofeedback
Chiaki Nishimura a,⁎, Li-Qun Wang b, Aki Nagase a,
Kazuko Terada a, Yoshifumi Miyamoto c,
Hisayuki Tsukuma a, Masuo Muro a
a Toho University School of Medicine, Japan
b Research Center for Advanced Technologies, Tokyo Denki University, Japan
c Department of Mechanical Engineering, Osaka Sangyo University, Japan
Abstract. Biofeedback is an acquisition technique of self-regulation ability of an autonomic
function, of which we are normally unaware, through a series of training aided by an additional outer
feedback pathway. We proposed a mathematical model of biofeedback in which a learning system on
the conscious level learns characteristics of a subconscious regulation system corresponding to the
biological function. When the learning converges, the learning system itself becomes an inverse
system of the regulation system. Then, if a regulation command is put to the learning system on the
conscious level, it drives the regulation system strictly following the command without the outer
feedback pathway, which enables voluntary control of the biological function. © 2007 Elsevier B.V.
All rights reserved.
Keywords: Biofeedback; Learning; Mathematical model; Autonomic function; Self-regulation
www.elsevier.com

2008-02-03T22:25:00.000+03:30

2008-02-03T22:17:00.000+03:30

Biofeedback systems architecture.
Paolini F, Bosetto A.
Hospal-Dasco SpA, Medolla, Italy. francesco.paolini@gambro.com

The capability for a dialysis machine to use a measurement of the patient's status to automatically tune the dialysis session on-line is commonly addressed by physicians and bioengineers working in the hemodialysis field as "biofeedback." This paper presents the basics of mathematical modeling and control theory normally used in bioengineering, together with some advanced techniques, such as adaptive and multi-input/multi-output control systems. The architectural requirements for implementing biofeedback techniques in renal replacement therapy are then discussed, with due attention paid to the safety aspects, which play a central role in machines hosting such new techniques as well as their therapeutic mission. Finally, the blood volume tracking system, which is aimed at performing the intradialytic water removal, while maintaining a balance inside the body fluids compartments and thus preserving cardiovascular stability, is used as a paradigmatic example of such a class of advanced techniques. The significant results shown by the blood-volume-controlled treatments during a multicenter study focused on its clinical application (30% reduction of intradialysis collapses, 13% reduction of interdialysis symptoms) indicate the technical feasibility and the remarkable benefits of such systems, which get closer to a structurally complete artificial kidney.

www.pubmed.gov

2008-02-03T21:13:00.000+03:30

Mathematical modeling of human cardiovascular system for simulation of orthostatic response
F. M. Melchior, R. S. Srinivasan and J. B. Charles
Laboratoire de Medecine Aerospatiale, Centre d'Essais en Vol, Bretigny S/Orge, France.

This paper deals with the short-term response of the human cardiovascular system to orthostatic stresses in the context of developing a mathematical model of the overall system. It discusses the physiological issues involved and how these issues have been handled in published cardiovascular models for simulation of orthostatic response. Most of the models are stimulus specific with no demonstrated capability for simulating the responses to orthostatic stimuli of different types. A comprehensive model incorporating all known phenomena related to cardiovascular regulation would greatly help to interpret the various orthostatic responses of the system in a consistent manner and to understand the interactions among its elements. This paper provides a framework for future efforts in mathematical modeling of the entire cardiovascular system.

http://ajpheart.physiology.org

2008-02-03T20:53:00.000+03:30

Human-System Modeling:
Some Principles and a Pragmatic Approach
Michael A. Freed & Michael G. Shafto
Cognition Research Group
Human-Automation Integration Research Branch
NASA-Ames Research Center
mfreed@mail.arc.nasa.gov
mshafto@mail.arc.nasa.gov
Abstract
There are a number of formalisms and architectures for modeling human performance, but
there is little guidance on how to go about building useful human models. This is a serious
problem since human modeling is difficult and full of pitfalls. The intended application of the
model should play a strong guiding role in model development. We are building an
engineering model intended to help interface designers predict usability problems -- in
particular, to alert designers to features of an interface that may increase the risk of certain
kinds of human error. In reflecting on our experience in building this model, we have
developed several inter-related principles that have been helpful in directing our investment of
time and effort. Taken together, these principles suggest a methodology for the development
of human performance models for complex human-machine systems.
www.siencdirect.com

2008-02-03T20:49:00.000+03:30

MODELING INSTABILITY IN THE CONTROL SYSTEM FOR
HUMAN RESPIRATION: APPLICATIONS TO INFANT NON-REM
SLEEP J. J. BATZELy AND H. T. TRANz
Abstract. Mathematical models of the human respiratory control system have been developed
since 1940 to study a wide range of features of this complex system. The phenomena collectively
referred to as periodic breathing (including Cheyne Stokes respiration and apneustic breathing) have
important medical implications. The hypothesis that periodic breathing is the result of delay in the
feedback signals to the respiratory control system has been studied since the work of Grodins et al.
in the early 1950's [36]. The purpose of this paper is to extend the model presented by Khoo et al.
[60] in 1991 to include variable delay in the feedback control loop and to study the phenomena of
periodic breathing and apnea as they occur during quiet sleep in infant sleep respiration at around
4 months of age. The nonlinear mathematical model consists of a feedback control system of ve
delay dierential equations. Numerical simulations are performed to study instabilities in the control
system and the occurence of periodic breathing and apnea in the above case which is a time frame
of high incidence of sudden infant death syndrome (SIDS).
www.elsevior.com

2008-02-02T14:06:00.000+03:30

A THREE-DIMENSIONAL HUMAN BODY
MODELING SYSTEM
Derya PAKALIN
August, 2002
IZMIR
ABSTRACT
The focal point of this study is to study on human body modeling systems. It is
related about the construction of complete, three-dimensional representations of the
normal male and female human bodies in the computer environment. In this study, a
human body modeling system has been developed to define 3D models of the whole
human body. The system reads a new type file HBM (Human Body Model) as input
and uses triangular meshes to generate a parametric surface model to describe the
human body surface. In computer graphics, triangular meshes are a very standard
way of representing 3D surfaces sets of any object. The system also shows a set of
conceptual parameters to allow the users to modify the body size of the models in a
controllable way. A significant design issue of such a system is to find a reasonable
compromise between visual realism, ease of control and rendering speed. For reasons
of the inherent difficulty of accurately modeling an entity as complex as the human
body, the system requires improved computer graphics and modeling techniques,
complex algorithms, faster machines and 3D scanners.
http://www.elsevier.com

2008-02-02T14:03:00.000+03:30

Electroencephalography & Neurofeedback
A Brief Introduction to the Science of Brainwaves
Glyn Blackett
Introduction
This article is a brief introduction to
electroencephalography or EEG, and its relevance
to therapy with neurofeedback. Neurofeedback is
an attempt to train or condition the EEG through
feedback, in the hope of alleviating symptoms.
EEG is a complex field and this introduction will
necessarily leave out much of the detail.
Nonetheless I hope it will provide a useful
background for people thinking of beginning
neurofeedback.
www.springer.com

2008-02-02T14:01:00.000+03:30

Neocortical Dynamics: Implications for
Understanding the Role of Neurofeedback and
Related Techniques for the Enhancement of Attention
Joel F. Lubar1
For nearly 25 years, EEG biofeedback (neurofeedback) has been utilized in research and
clinical settings for the treatment and investigation of a number of disorders ranging from
attention deficit hyperactivity disorder to seizure disorders as well as many other established
and investigational applications. Until recently, mechanisms underlying the generation and
origins of EEG have been poorfy understood but now are beginning to become much man;
clarified Now it is important to combine the information gathered on the genesis of EEG
and neocortical dynamics with the findings from neurofeedback investigations. This will help
us to develop models of how neurofeedback might operate in producing the changes in EEG
and in clinical symptomatology. We know that the cortex operates in terms of resonant loops
between neocortical columns of cells known as local, regional, and global resonances. These
resonances determine the specific EEG frequencies and are often activated by groups of cells
in the thalamus known as pacemakers. There are complex excitatory and inhibitory
interactions within the cortex and between the cortex and the thalamus that allow these loops
to operate and provide the basis for learning. Neurofeedback is a technique for modifying
these resonant loops, and hence, modifying the neurophysiological and neurological basis for
learning and for the management of a number of neurologically based disorders. This paper
provides an introduction to understanding EEC and neocortical dynamics and how these
concepts can be used to explain the results of neurofeedback training and other interventions
particularly in the context of understanding attentive mechanisms and for the management
of attention deficit/hyperactivity disorders.
KEY WORDS: words: neocortical dynamics; neurofeedback; attention; ADHD; ADD
From www.springer.com

2008-02-02T13:59:00.000+03:30

2008-02-02T13:35:00.000+03:30

Self-Emergence of Chaos in Identifying Irregular Periodic Behavior
Oscar DE FEO
Laboratory of Nonlinear Systems
Swiss Federal Institute of Technology Lausanne
EL-E, EPFL-I&C-LANOS, CH-1015 Lausanne, Switzerland
Phone:+41-21-693-5683, Fax:+41-21-693-6700
Email: Oscar.DeFeo@epfl.ch
Abstract — In order to exploit generalized chaotic synchronization
phenomena for the solution of temporal pattern
recognition problems, a chaotic dynamical system representing
the class of signals that are to be recognized must be established.
This system can be determined by means of identification
techniques. Although the fulfillment of the chaotic
condition could appear as a constraint, it is shown here that,
for a very simple identification algorithm, chaos self-emerges
when a model, fitting unprecise periodic signals, is identified
From www.elsevior.com

2008-02-02T13:25:00.000+03:30

High-order representation of Poincare´ maps
Johannes Grote, Martin Berz, Kyoko Makino
Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
Available online 23 January 2006
Abstract
A method to obtain DA approximations of Poincare´ maps directly from a DA approximation of the flow of the differential equation
for certain types of flows and Poincare´ sections is presented. Examples of the performance of the method, its computational
implementation, and its use for problems in beam physics are given.
r 2006 Elsevier B.V. All rights reserved.
Keywords: Poincare´ map; Differential algebra
From www.siencedirect.com

2008-02-02T13:24:00.000+03:30

Enhancing Poincare plot information via sampling ratesR.A. Thuraisingham
1A, Russell Street, Eastwood, Sydney, NSW 2122, Australia
Abstract
Poincare plots of a continuous solution of the logistic equation at different sampling rates are studied. The study uses
the continuous solution obtained for the parameter A = 4 in the logistic equation. This solution of the logistic equation
used in this study provides a useful handle to study sampling effects and at the same time look at a system which exhibits
complex correlations. The results of this study show that the Poincare plots of a continuous function at different sampling
rates provide valuable information about the complex correlations present in the system. This additional information provided
by the Poincare plots of data from a continuous system sampled at different rates will be a useful and simple way of
studying correlations present in a real system with applications in biomedicine.
2006 Elsevier Inc. All rights reserved.
Keywords: Poincare plot; Sampling rate; Logistic equation; Correlations
From www.siencedirect.com

2008-02-02T13:22:00.000+03:30

Applications of the Poincare´ mapping technique
to analysis of neuronal dynamicsPaul Channell Jr.a, Gennady Cymbalyukb, Andrey Shilnikova,
aDepartment of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA
bDepartment of Physics and Astronomy, Georgia State University, Atlanta, GA 30303, USA
Available online 9 November 2006
Abstract
A single neuron can demonstrate different spiking and bursting patterns which can be elicited naturally depending on modulation
status or artificially due to disturbances caused by distinct recording techniques. For example, when pharmacologically isolated with
bicuculline a leech oscillatory heart interneuron can show an endogenous bursting activity while recorded extracellularly, or the periodic
tonic spiking activity while recorded intracellularly. Transitions between these oscillatory patterns are in general non-local and could not
be understood using only the local analysis of the neuron’s rest states, but the global theory tools such as the Poincare´ return mapping
analysis. The mappings constructed then predict the temporal characteristics of the spiking and bursting patterns and allow one to study
transitions between them. The technique is directly applicable to neuronal models of various types, as well as is aimed to be employed in
neurophysiological experiments.
r 2006 Elsevier B.V. All rights reserved.
Keywords: Tonic spiking; Bursting neuron; Active transitions; Poincare´ mapping
From www.siencedirect.com

2008-02-02T13:21:00.000+03:30

A novel chaotic attractorChongxin Liu
Institute of Electrical Engineering, Xi’an Jiaotong University, State Key Laboratory of Electrical Insulation
and Power Equipment, Xi’an 710049, PR China
Accepted 10 April 2007
Abstract
In this letter, a novel chaotic attractor is reported. Some basic dynamical properties, such as Lyapunov exponents,
fractal dimension, Poincare mapping, the continuous spectrum and chaotic behavior of this new transverse butterfly
attractor are studied. Meanwhile, the forming mechanism of its compound structure obtained by merging together
two simple attractors after performing one mirror operation has been investigated by detailed numerical as well as theoretical
analysis. Furthermore, the complex chaotic dynamical behavior of the system has been also proofed by experimental
simulation of a designed electronic oscillator based on EWB.
2007 Published by Elsevier Ltd
From www.siencedirect.com

2008-02-02T13:20:00.000+03:30

On computing Poincare´ map by He´non method
P. Palaniyandi
Centre for Nonlinear dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
Accepted 20 June 2007
Abstract
The trajectory of the autonomous chaotic system deviates from the original path leading to a deformation in its
attractor while calculating Poincare´ map using the method presented by He´non [He´non M. Physica D 1982;5:412].
Also, the Poincare´ map obtained is found to be the Poincare´ map of deformed attractor instead of the original attractor.
In order to overcome these drawbacks, this method is slightly modified by introducing an important change in the existing
algorithm. Then it is shown that the modified He´non method calculates the Poincare´ map of the original attractor
and it does not affect the system dynamics (attractor). The modified method is illustrated by means of the Lorenz and
Chua systems.
2007 Elsevier Ltd. All rights reserved
From www.elsevier.com

2008-02-02T13:11:00.001+03:30

Population Floors and the Persistence of Chaos
in Ecological मोदेल्स
Graeme D. Ruxton
Division of Environmental 6 Evolutionary Biology, Graham Kerr Building,
University of Glasgow, Glasgow G12 8QQ, United Kingdom
and
Pejman Rohani
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA*
Received March 27, 1996
Chaotic dynamics have been observed in a wide range of population models. Here we
describe the effects of perturbing several of these models so as to introduce a non-zero mini-
mum population size. This perturbation generally reduces the likelihood of observing chaos, in
both discrete and continuous time models. The extent of this effect depends on whether chaos
is generated through period-doubling, quasiperiodicity, or intermittence. Chaos reached via
the quasiperiodic route is more robust against the perturbation than period-doubling chaos,
whilst the inclusion of a population floor in a model exhibiting intermittent chaos may increase
the frequency of population bursts although these become non-chaotic. ] 1998 Academic Press
From www.siencedirect.com

2008-02-02T13:11:00.000+03:30

Population Floors and the Persistence of Chaos
in Ecological मोदेल्स
Graeme D. Ruxton
Division of Environmental 6 Evolutionary Biology, Graham Kerr Building,
University of Glasgow, Glasgow G12 8QQ, United Kingdom
and
Pejman Rohani
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA*
Received March 27, 1996
Chaotic dynamics have been observed in a wide range of population models. Here we
describe the effects of perturbing several of these models so as to introduce a non-zero mini-
mum population size. This perturbation generally reduces the likelihood of observing chaos, in
both discrete and continuous time models. The extent of this effect depends on whether chaos

is generated through period-doubling, quasiperiodicity, or intermittence. Chaos reached via
the quasiperiodic route is more robust against the perturbation than period-doubling chaos,
whilst the inclusion of a population floor in a model exhibiting intermittent chaos may increase
the frequency of population bursts although these become non-chaotic. ] 1998 Academic Press
From www.siencedirect.com

2008-01-30T01:02:00.000+03:30

Observation of Crises and Bifurcations in the
Hodgkin-Huxley Neuron Model
Wuyin Jin1, Qian Lin2, Yaobing Wei1, and Ying Wu3
1 College of Mechano-Electronic Engineering,
Lanzhou University of Technology, Lanzhou 730050, China
jinwuyin@263.net
2 College of Petrochemical Technology, Lanzhou University of Technology,
Lanzhou 730050, China
3 College of Science, Lanzhou University of Technology,
Lanzhou 730050, China
Abstract. With the changing of the stimulus frequency, there are a lot
of firing dynamics behaviors of interspike intervals (ISIs), such as quasiperiodic,
bursting, period-chaotic, chaotic, periodic and the bifurcations
of the chaotic attractor appear alternatively in Hodgkin-Huxley (H-H)
neuron model. The chaotic behavior is realized over a wide range of
frequency and is visualized by using ISIs, and many kinds of abrupt undergoing
changes of the ISIs are observed in deferent frequency regions,
such as boundary crisis, interior crisis and merging crisis displaying alternately
along with the changes changes of external signal frequency,
too. And there are many periodic windows and fractal structures in ISIs
dynamics behaviors. The saddle node bifurcation resulted collapses of
chaos to period-12 orbit in dynamics of ISIs is identified.
From www.elsevier.com

2008-01-30T00:57:00.000+03:30

Aperiodic flow-induced oscillations of collapsible tubes:
a critical reappraisalC.D. Bertram a,, J. Timmer b, T.G. Mu¨ ller b, T. Maiwald b, M. Winterhalder b,
H.U. Voss b
a Graduate School of Biomedical Engineering, University of New South Wales, Sydney, NSW 2052, Australia
b Freiburger Zentrum fu¨ r Datenanalyse und Modellbildung, Fakulta¨t fu¨ r Physik, Albert–Ludwigs–Universita¨ t Freiburg, Eckerstraße 1, 79 104
Freiburg, Germany
Received 7 April 2003; received in revised form 14 October 2003; accepted 21 November 2003
Abstract
The evidence for the aperiodic self-excited oscillations of flow-conveying collapsible tubes being mathematically chaotic is reexamined.
Many cases which powerfully suggest nonlinear deterministic behaviour have not been recorded over time-spans which
allow their exhaustive examination. The present investigation centred on a previously recorded robust and generic oscillation, but
more recent and more discerning tests were applied. Despite hints that a low embedding dimension might suffice, the data
appeared on most indices high-dimensional. A U-shaped return map was found and modelled using both radial basis functions
and polynomials, but lack of detailed structure in the map prevented effective parameter estimation. On the basis of power-law
rather than exponential divergence of nearby trajectories, and of inability to discriminate against behaviour which would also be
manifested by a surrogate consisting of a noise-perturbed nonlinear periodic oscillator, it is concluded that the data do not support
the idea that the aperiodicity in the particular oscillation examined is caused by deterministic chaos. There was evidence that
the distributed nature of the physical system might underlie aspects of the high dimensionality. We advocate equally searching
testing of any future candidate chaotic oscillations in the investigation of collapsed-tube flows.
# 2003 IPEM. Published by Elsevier Ltd. All rights reserved.
Keywords: Nonlinear dynamics; Deterministic chaos; Time-series analysis; Self-excited oscillation
From www.elsevior.com

2008-01-30T00:48:00.000+03:30

Chaotic Title

Self-Emergence of Chaos in Identifying Irregular Periodic Behavior
Oscar DE FEO
Laboratory of Nonlinear Systems
Swiss Federal Institute of Technology Lausanne
EL-E, EPFL-I&C-LANOS, CH-1015 Lausanne, Switzerland
Phone:+41-21-693-5683, Fax:+41-21-693-6700
Email: Oscar.DeFeo@epfl.ch
Abstract — In order to exploit generalized chaotic synchronization
phenomena for the solution of temporal pattern
recognition problems, a chaotic dynamical system representing
the class of signals that are to be recognized must be established.
This system can be determined by means of identification
techniques. Although the fulfillment of the chaotic
condition could appear as a constraint, it is shown here that,
for a very simple identification algorithm, chaos self-emerges
when a model, fitting unprecise periodic signals, is identified.
From www.elsevior.com