EMERGENT CHAOS SYNCHRONIZATION IN NONCHAOTIC CNNS

2008 ◽  
Vol 18 (05) ◽  
pp. 1337-1342 ◽  
Author(s):  
XIAO-SONG YANG ◽  
QUAN YUAN
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Chaos Synchronization ◽  
Chaotic Dynamics ◽  
Cellular Neural Networks ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable

It is shown that emergent chaos synchronization can take place in coupled nonchaotic unit dynamical systems. This is demonstrated by coupling two nonchaotic cellular neural networks, in which the couplings give rise to a synchronous chaotic dynamics and in the meanwhile the synchronous dynamics is globally asymptotically stable, thus chaos synchronization takes place under the suitable couplings.

Study on Discreted Fifth-Order CNN Hyper-Chaos Synchronization Reduced Order Observer

2011 ◽  
Vol 135-136 ◽  
pp. 960-963
Author(s):  
Jie Xu ◽  
Juan Chang ◽  
Lian Zhang ◽  
Yong Sun
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
State Observer ◽  
Cellular Neural Networks ◽  
Reduced Order ◽  
Reduced Order Observer ◽  
Fifth Order ◽  
Order State

Secure communication with the hyper-chaos synchronization approach is the popular investigation. In this paper the fifth-order Cellular Neural Networks(CNN) hyper-chaos equation of continuous time was discreted. The innovation was that the synchronization of the hyper-chaos system was realized with the discreted reduced order state observer. Finally, the system stabilizing to zero after fugacious transition and achieving synchronization were validated by simulations, which showed the algorithm’s availability.

BIFURCATIONS AND OSCILLATORY BEHAVIOR IN A CLASS OF COMPETITIVE CELLULAR NEURAL NETWORKS

2000 ◽  
Vol 10 (06) ◽  
pp. 1267-1293 ◽  
Author(s):  
M. DI MARCO ◽  
A. TESI ◽  
M. FORTI
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Opposite Sign ◽  
Symmetric Matrix ◽  
General Theorem ◽  
Dynamical Behavior ◽  
Cellular Neural Networks ◽  
Oscillatory Behavior ◽  
Third Order ◽  
Small Perturbations

When the neuron interconnection matrix is symmetric, the standard Cellular Neural Networks (CNN's) introduced by Chua and Yang [1988a] are known to be completely stable, that is, each trajectory converges towards some stationary state. In this paper it is shown that the interconnection symmetry, though ensuring complete stability, is not in the general case sufficient to guarantee that complete stability is robust with respect to sufficiently small perturbations of the interconnections. To this end, a class of third-order CNN's with competitive (inhibitory) interconnections between distinct neurons is introduced. The analysis of the dynamical behavior shows that such a class contains nonsymmetric CNN's exhibiting persistent oscillations, even if the interconnection matrix is arbitrarily close to some symmetric matrix. This result is of obvious relevance in view of CNN's implementation, since perfect interconnection symmetry in unattainable in hardware (e.g. VLSI) realizations. More insight on the behavior of the CNN's here introduced is gained by discussing the analogies with the dynamics of the May and Leonard model of the voting paradox, a special Volterra–Lotka model of three competing species. Finally, it is shown that the results in this paper can also be viewed as an extension of previous results by Zou and Nossek for a two-cell CNN with opposite-sign interconnections between distinct neurons. Such an extension has a significant interpretation in the framework of a general theorem by Smale for competitive dynamical systems.

COMPLETE STABILITY FOR A CLASS OF CELLULAR NEURAL NETWORKS

2001 ◽  
Vol 11 (01) ◽  
pp. 169-177 ◽  
Author(s):  
CHIH-WEN SHIH
Keyword(s):  
Neural Networks ◽  
Vector Field ◽  
Dynamical Systems ◽  
State Vector ◽  
Cellular Neural Networks ◽  
Output Function ◽  
Output Vector ◽  
Liapunov Functions ◽  
Lattice Dynamical Systems ◽  
Invariant Principle

This work investigates a class of lattice dynamical systems originated from cellular neural networks. In the vector field of this class, each component of the state vector and the output vector is related through a sigmoidal nonlinear output function. For two types of sigmoidal output functions, Liapunov functions have been constructed in the literatures. Complete stability has been studied for these systems using LaSalle's invariant principle on the Liapunov functions. The purpose of this presentation is two folds. The first one is to construct Liapunov functions for more general sigmoidal output functions. The second is to extend the interaction parameters into a more general class, using an approach by Fiedler and Gedeon. This presentation also emphasizes the complete stability when the equilibrium is not isolated for the standard cellular neural networks.

scholarly journals ON DIFFUSION DRIVEN OSCILLATIONS IN COUPLED DYNAMICAL SYSTEMS

1999 ◽  
Vol 09 (04) ◽  
pp. 629-644 ◽  
Author(s):  
ALEXANDER POGROMSKY ◽  
TORKEL GLAD ◽  
HENK NIJMEIJER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Threshold Value ◽  
Oscillatory Behavior ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nonminimum Phase ◽  
Nonminimum Phase Systems ◽  
Diffusive Medium ◽  
Phase Systems

The paper deals with the problem of destabilization of diffusively coupled identical systems. Following a question of Smale [1976], it is shown that globally asymptotically stable systems being diffusively coupled, may exhibit oscillatory behavior. It is shown that if the diffusive medium consists of hyperbolically nonminimum phase systems and the diffusive factors exceed some threshold value, the origin of the overall system undergoes a Poincaré–Andronov–Hopf bifurcation resulting in oscillatory behavior.

STABILITY OF EQUILIBRIA OF NEURAL NETWORKS

1999 ◽  
Vol 09 (10) ◽  
pp. 1941-1955
Author(s):  
P. F. CURRAN ◽  
L. O. CHUA
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Special Class ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Stability Of Equilibria

Sufficient conditions for local and global asymptotic stability of equilibria of some general classes of neural networks are presented. In the event that the interconnection matrix is block diagonally stable it is shown that the equilibrium is globally asymptotically stable if the cells are dissipative at the equilibrium. For a special class of networks the conditions of dissipativity are reduced to more readily-tested conditions of passivity. Equilibria are shown to be asymptotically stable essentially if the cells are locally passive.

scholarly journals A NEW TYPE OF SELF-ORGANIZATION ASSOCIATED WITH CHAOTIC DYNAMICS IN NEURAL NETWORKS

1996 ◽  
Vol 07 (04) ◽  
pp. 451-459 ◽  
Author(s):  
I. TSUDA
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Chaotic Dynamics ◽  
Complex Dynamics ◽  
The Other ◽  
Self Organization ◽  
High Dimensional ◽  
Self Organized ◽  
New Type ◽  
Contraction Dynamics

A new type of self-organized dynamics is presented, in relation with chaos in neural networks. One is chaotic itinerancy and the other is chaos-driven contraction dynamics. The former is addressed as a universal behavior in high-dimensional dynamical systems. In particular, it can be viewed as one possible form of memory dynamics in brain. The latter gives rise to singular-continuous nowhere-differentiable attractors. These dynamics can be related to each other in the context of dimensionality and of chaotic information processings. Possible roles of these complex dynamics in brain are also discussed.

The characteristics of nonlinear chaotic dynamics in quantum cellular neural networks

2008 ◽  
Vol 17 (8) ◽  
pp. 2837-2843 ◽  
Author(s):  
Wang Sen ◽  
Cai Li ◽  
Kang Qiang ◽  
Wu Gang ◽  
Li Qin
Keyword(s):  
Neural Networks ◽  
Chaotic Dynamics ◽  
Cellular Neural Networks
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