Authors: None

Abstract:

Keywords:

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.90001

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: ---

Authors: None

Abstract:

Keywords:

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.90002

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: ---

Authors: Archer, Daan; Van Someren, Maarten; Van Leeuwen, Cees

Abstract: In trying to establish neurally plausible models of human information processing, the connectionist movement failed because their models lacked interesting dynamics. We propose that coupled maps offer neurodynamically more plausible tools for modeling cognitive phenomena. Activity in coupled maps shows dynamic synchronization behavior that is phenomenally similar to large-scale brain activity. It is possible to tweak this behavior to enable reading-in of spatially patterned information, and to engineer mechanisms for encoding storage of these patterns. Previous work showed how these solutions lead to simple explanations of a number of phenomena observed in human visual perception, including some visual illusions and multi-stability; and in memory, such as iconic storage, slow decay, and spontaneous re-instantiation. The present work explores dynamic weight adjustment at multiple time scales simultaneously, in particular its possible utility for memory retrieval and read-out of patterned information.

Keywords: logistic maps,dynamical synchronization,neural networks,iconic storage,forgetting curves,spontaneous recall,priming,retrieval

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00003

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 1-4

Authors: Kazantsev, Victor B.; Mukhina, Irina V.; Zaytsev, Yury V.; Galkina, Marina O.

Abstract: Oscillatory spiking activity of neuronal networks as possible mechanism of information representation and encoding is a subject of intensive discussions in experimental and mathematical neuroscience. Self-sustained network spiking patterns may appear due to the presence of local oscillatory cells (pacemakers) continuously stimulating their neighbors through the synaptic couplings. Alternatively, the patterns may be induced by a constant external drive (rhythmic or noisy signals) providing sequential excitations of the network cells. We consider the network of originally nonoscillatory neurons and analyze the possibility of spontaneous spiking due to cycling excitations along closed routes or loops. As a biological background we use experimental data of neuronal culture activity recorded by multielectrode array (MEA) technology. As a mathematical model we construct a network of synaptically coupled Hodgkin-Huxley neurons with relatively small number of cells interacting by full graph topology of synaptic excitatory/inhibitory couplings. We show that there is a critical coupling strength above which the network starts to generate self-sustained spiking patterns. Using a cross-correlation analysis of model data we identify simple local excitation routes in the form of correlated spiking events.

Keywords: neural networks,neural activity,synfire patterns,synchronization,nonlinear theory

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00004

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 5-10

Authors: Pototsky, Andrey; Janson, Natalia

Abstract: We consider a two-state stochastic process with time delayed feedback which implies history-dependent residence time distributions (RTDs). The equilibrium RTD in the sense of the averaging over all possible histories is introduced. We use the path integral representation to link the equilibrium RTD to the distribution function of the history. Equilibrium RTD is determined analytically for small and intermediate delay times. Analytic results are compared with numerical simulations of a bistable system with two time delays.

Keywords: stochastic processes,delay,control

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00005

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 11-15

Authors: Borisyuk, Roman

Abstract: A biologically realistic neural network model of the tadpole spinal cord has been design. Morris-Lecar model of a single neuron is used to describe the spike generation. A bifurcation analysis of two inhibitory coupled Morris-Lecar elements with post-inhibitory rebound provides a range of parameters where anti-phase oscillations exist. A simple model of axon growth with deterministic and stochastic components allows to generate a complete biologically realistic architecture of neuronal connectivity of the tadpole spinal cord. We use this architecture of interconnected Morris-Lecar elements with randomly distributed parameter values to demonstrate that the neural network can generate a specific pattern of neural activity corresponding to the tadpole swimming.

Keywords: neural activity,spiking model of neuron,neural connections

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00006

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 16-20

Authors: Steur, Erik; Tyukin, Ivan; Nijmeijer, Henk

Abstract: We discuss synchronization in networks of neuronal oscillators which are linearly coupled via gap junctions. We show that the neuronal models of Hodgkin-Huxley, Morris-Lecar, FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (electrical) energy is bounded. As a result, for a wide range of coupling configurations, networks of these oscillators will posses ultimately bounded solutions. Moreover, when the coupling is strong enough the oscillators become synchronized. We demonstrate the synchronization of Hindmarsh-Rose oscillators by means of a computer simulation.

Keywords: neural dynamics,networks,synchronization

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00007

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 21-26

Authors: Vepa, Ranjan

Abstract: In this paper an array of non-identical, locally connected chaotic biological neurons are modelled by a single representative chaotic neuron model based on an extension of the Hindmarsh-Rose neuron. This model is then employed in conjunction with the unscented Kalman filter to study the associated state estimation problem. The archetypal system, which was deliberately chosen to be chaotic, was corrupted with noise. The influence of noise seemed to kill the chaotic behaviour. Consequently it was observed that the filter performs quite well in reconstructing the states the system although the introduction of relatively low noise had a profound effect on the system. Neither the noise corrupted process model nor the filter gave any indications of chaos. We believe that this behaviour can be generalised and expect that unscented Kalman filtering of the states of a biological neuron to be completely feasible even when the uncorrupted process model exhibits chaos.

Keywords: chaotic behaviour,neural control,estimator,Kalman filters

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00008

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 27-32

Authors: Karimi, Hamid Reza; Zapateiro, Mauricio; Luo, Ningsu

Abstract: This paper investigates the delay-dependent adaptive synchronization problem of the master and slave structure of linear systems with both constant neutral and time-varying discrete time-delays and nonlinear perturbations based on the Barbalat lemma and matching conditions. An adaption law which includes the master-slave parameters is obtained by using the Lyapunov functional method and inequality techniques to synchronize the master-slave systems without the knowledge of upper bounds of perturbation terms. Particularly, it is shown that the synchronization speed can be controlled by adjusting the update gain of the synchronization signal. A numerical example has been given to show the effectiveness of the method.

Keywords:

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00009

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 33-38

Authors: Del Campo, O. R. Acosta; Cruz-Hernández, C.; López-Gutiérrez, R. M.; Garcia-Guerrero, E. E.

Abstract: In this paper, we use a Generalized Hamiltonian systems approach to synchronize a modified Chua's circuit, which generates hyperchaotic dynamics. Synchronization is obtained between the master and slave dynamics with the slave being given by an observer. We apply this approach to transmit private information signals in which the quality of the recovered signal is higher than in traditional observer techniques while the encoding remains potentially secure.

Keywords: hyperchaos synchronization,modified fourth-order Chua's circuit,generalized Hamiltonian forms,observers,secure communication

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00010

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 39-44

Authors: Buscarino, Arturo; Fortuna, Luigi; Frasca, Mattia

Abstract: In this work we study synchronization in presence of parameter mismatches between two coupled hyperchaotic circuits. A master-slave scheme based on negative feedback [Kapitaniak et al. (1994)] is considered, where the slave system is designed as an observer of the master. The choice of the observer gains is based on the Master Stability Function in the case that the two circuits are coupled through a unique scalar signal. The approach is experimentally validated, showing how synchronization widely occurs in the range of electronic component tolerances.

Keywords: hyperchaos,nonlinear dynamics,synchronization,robustness,circuits

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00011

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 45-49

Authors: De Lellis, Pietro; Di Bernardo, Mario

Abstract: We discuss a novel approach to synchronization of complex networks based on the use of a hybrid adaptive strategy where the coupling gains between neighbouring oscillators are time-varying and the links of the network become activated only when certain conditions are satisfied. We study the novel strategy on some representative examples showing its viability and effectiveness in achieving synchronization. The emerging network topologies are studied and compared via appropriate numerical simulations.

Keywords: synchronization,adaptive gains,networks,hybrid systems,chaotic behaviour

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00012

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 50-55

Authors: Suzuki, Masayasu; Sakamoto, Noboru; Naito, Kazutoshi

Abstract: We try to stabilize steady solutions of a physical model described by wave equations with nonlinear boundary conditions. This system is a distributed parameter system in which ideal turbulence, introduced by Sharkovsky et al., occurs. Although the behavior of the system is quite intricate both in time and space, by using the d'Alembert's solution, the analysis of the dynamic characteristics can be reduced to that of a finite-dimensional difference equation. In this report, based on this analytical method using the d'Alembert's solution, we design control laws to stabilize steady solutions and synchronize a pair of the distributed parameter systems. And then, we show that the stabilization and the synchronization can be accomplished only by boundary inputs.

Keywords: chaos,ideal turbulence,stabilization,synchronization,wave equations,boundary conditions

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00013

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 56-61

Authors: Camplani, M.; Cannas, B.; Carboni, P.

Abstract: In this paper, the dynamics of a nonlinear bidirectional coupling of two Lorenz systems is analyzed. The coupling is realized trough polynomial functions composed by quadratic terms of the system state variables. The analysis of the transverse and tangent systems ensures the absence of synchronization between the subsystems. It is demonstrated that with this choice of the coupling functions, the system dynamics is not hyperchaotic in spite of the presence of two positive Lyapunov exponents.

Keywords: coupled systems,synchronization,Lyapunov exponents,hyperchaos

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00014

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 62-66

Authors: Buscarino, Arturo; Fortuna, Luigi; Frasca, Mattia; Sciuto, Gregorio

Abstract: In this paper, the experimental synchronization of chaotic circuits with different dynamical behavior is taken into account. Starting from both qualitative and quantitative considerations, a procedure, based on linear matrix inequalities, to assess the necessary condition for the synchronization of non-identical circuits is discussed. The results obtained are then evaluated through an experimental approach showing the synchronization of chaotic circuits differing either in parameter values or in their dynamical equations.

Keywords: chaos,synchronization,nonlinear systems,LMI,electronic circuits

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00015

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 67-70

Authors: Kowalczyk, Piotr; Sieber, Jan

Abstract: In the paper we consider how orbits characterised by the presence of so-called sliding motion, which orbits typically occur in hybrid systems of Filippov type, are affected by stable singular perturbations. To be able to pursuit our analysis we consider a planar minimal system and we tune a system parameter such that a stable periodic orbit of the system touches the discontinuity surface: this is the so-called grazing-sliding bifurcation. We then check the effect of stable singular perturbation on the grazing cycle. In the unperturbed system the periodic orbit remains stable, and its local return map becomes piecewise linear. The effect of an arbitrarily small stable singular perturbation is that the local return map changes qualitatively, giving rise to, for example, period-adding cascades or small-scale chaos.

Keywords: hybrid systems,chaos,robustness,grazing-sliding bifurcations

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00016

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 71-75

Authors: Ing, James; Pavlovskaia, Ekaterina; Wiercigroch, Marian

Abstract: A linear oscillator undergoing impact with a secondary support is studied numerically. Smooth as well as nonsmooth bifurcations are observed. The bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces. The obtained results are verified by comparison with previous experimental studies. Experimental stability analysis is also presented, justifying the normal form maps used to show the response close to grazing for systems with and without prestress of the secondary spring. The high degree of correspondence lends support to the modelling approach, as does the close match between experiments and simulations.

Keywords: piecewise linear oscillator,grazing,experimental,stability

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00017

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 76-80

Authors: Jeffrey, Mike R.

Abstract: In a three dimensional dynamical system with a discontinuity along a codimension one switching manifold, orbits of the system may be tangent to both sides of the switching manifold generically at isolated points. It is perhaps surprising, then, that examples of such 'two-fold' singularities are difficult to find amongst physical models. They occur where the relative curvature between the flow field and the switching manifold is nonsymmetric about the discontinuity. Here we motivate their study with a local form model of nonlinear control that exhibits the two-fold singularity, where the flow is constant either side of a curved switching manifold. We describe the local dynamics around general two-fold singularities, then consider their effect on global dynamics via one parameter bifurcations of limit cycles.

Keywords: singularities,sliding,discontinuous control,nonlinear control,switching

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00018

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 81-86

Authors: Navarro-López, Eva M.

Abstract: Although discontinuous, non-smooth or switched dynamical systems have been broadly studied, there still exist dynamical behaviours which are not completely understood. In particular, those related to transitions between state-space regions and to crossings through discontinuity surfaces. The problem of specifying system transitions becomes crucial when multiple discontinuity surfaces or switching elements are present. In this case, a great deal of care has to be taken in order to simulate the system and to verify its properties. Obtaining a computational model appears to be an elegant way for the specification of the transitions and event-triggered phenomena involved in the dynamical behaviour of discontinuous systems. This is the goal of this paper. A class of discontinuous dynamical systems including control inputs and outputs is reinterpreted within the hybrid-automata framework, and what is referred as to discontinuous-dynamical-system hybrid automaton is proposed. An example is used, which corresponds to a 2-degrees-of-freedom electromechanical system including discontinuous friction and sliding-mode control. This system exhibits several discontinuity surfaces which give rise to different types of transitions and dynamical behaviours. New computational-kind phenomena may arise when the system is reinterpreted as a hybrid dynamical system. Nevertheless, this paper only deals with the modelling and specification of the system.

Keywords: hybrid systems,discontinuous systems,hybrid automata,computational models,Friction,sliding motions,switching control,abstraction-based approach

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00019

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 87-92

Authors: Piiroinen, Petri T.; Mason, Joanna F.

Abstract: In this paper we analyse a dynamical system corresponding to a model of gear rattle. We highlight some of the rich dynamics that can be found in the vicinity of both smooth and nonsmooth bifurcations. In particular, we are interested in two completely different mechanisms in which the same chaotic attractor disappears, namely, through a grazing bifurcation and a homoclinic tangency.

Keywords: impact,piecewise-smooth dynamical system,bifurcation,grazing,stability,chaos

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00020

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 93-97

Authors: Colombo, A.; Dercole, F.

Abstract: We report novel results on three codimension-two bifurcations in nonsmooth systems, namely the border-fold, border-fiip, and border-Neimark-Sacker. These results, obtained in the discrete-time framework, are easily applicable in the analysis of Poincaré maps of periodic solutions in continuous-time. Three models, taken from different fields of science and engineering, are then briefly described and used as test benches for the theoretical results.

Keywords: bifurcation,border collision,codimension-two,non-hyperbolic,nonsmooth

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00021

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 98-103

Authors: Kharel, Rupak; Busawon, K.; Ghassemlooy, Z.

Abstract: In this work, a novel chaotic encryption technique is proposed to realize a secure communication system. In the proposed method, the message signal to be transmitted is first encrypted using a chaotic keystream and then modulated with a chaotic signal. At the receiver end, the received chaotic signal is used for synchronization and to recover the encrypted signal. After applying the same keystream used in transmitter side, the message signal could be decrypted back. The main contribution of this work is generation of the keystream which is not part of the transmitter chaotic oscillator but is produced using an oscillator of a different structure.

Keywords: chaotic cryptosystem,synchronization,secure communication

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00022

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 104-109

Authors: Liang, Xiyin; Zhang, Jiangfeng; Xia, Xiaohua

Abstract: An encryption algorithm based on a discretized chaotic map controlled by a Δ-modulated feedback is applied to a direct sequence code-division-multiple-access (DS-CDMA) scheme, which improves security at the cost of lowering the performance of bit error rate (BER). However, numerical simulations show that the DS-CDMA scheme still has a satisfactory performance by means of the spreading sequences generated by a continuous chaotic system. These spreading sequences are chosen from the local maximums of the output of the continuous chaotic system. This scheme is also robust against the channel noise.

Keywords: CDMA,spreading sequences,Lorenz system,bit error rate (BER),signal to noise ratio (SNR),Gram-Schmidt orthonormalization

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00023

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 110-115

Authors: Eisencraft, Marcio; Amaral, Marcos Almeida Do

Abstract: In this paper we compare two techniques applied to the estimation of discrete-time one-dimensional chaotic orbits: the maximum likelihood estimation and the modified Viterbi algorithm. As the second one performs better, it is used in two digital modulation schemes based on identification of chaos generator maps: the Modified Maximum Likelihood Chaos Shift Keying using one and two maps. Both have better symbol error rate characteristics than non-coherent chaos communication schemes.

Keywords: chaos,estimation algorithms,communications systems,white noise,nonlinear systems

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00024

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 116-121

Authors: Noura, Hassan; Henaff, Sebastien; Taralova, Ina; El Assad, Safwan

Abstract: In order to improve the communication security, two novel chaotic generators are proposed. The first one is a single order chaotic generator using two cascading stages, and the second one is a second order chaotic generator with single and cascaded layer. The goal is to generate binary pseudo random chaotic signal with high degree of randomness. We analyze their global dynamics properties using system and signal processing tools (Lyapunov exponents, bifurcation diagrams, distribution, pseudo phase, autocorrelation, cross correlation, NIST test). A complete analysis is provided. Experimental and theoretical analyses show that the proposed generators have good cryptographic properties.

Keywords:

Digital Object Identifier (DOI): 10.3182/20090622-3-UK-3004.00025

Conference: 2nd IFAC Conference on Analysis and Control of Chaotic Systems (2009)

Location: Queen Mary University of London, United Kingdom

Start Date: Mon Jun 22 2009 - End Date: Wed Jun 24 2009

Page Numbers: 122-127