3,431 research outputs found
Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic systems
In a recent paper, wavelet analysis was used to perturb the coupling matrix
in an array of identical chaotic systems in order to improve its
synchronization. As the synchronization criterion is determined by the second
smallest eigenvalue of the coupling matrix, the problem is
equivalent to studying how of the coupling matrix changes with
perturbation. In the aforementioned paper, a small percentage of the wavelet
coefficients are modified. However, this result in a perturbed matrix where
every element is modified and nonzero. The purpose of this paper is to present
some results on the change of due to perturbation. In particular,
we show that as the number of systems , perturbations which only
add local coupling will not change . On the other hand, we show that
there exists perturbations which affect an arbitrarily small percentage of
matrix elements, each of which is changed by an arbitrarily small amount and
yet can make arbitrarily large. These results give conditions on
what the perturbation should be in order to improve the synchronizability in an
array of coupled chaotic systems. This analysis allows us to prove and explain
some of the synchronization phenomena observed in a recently studied network
where random coupling are added to a locally connected array. Finally we
classify various classes of coupling matrices such as small world networks and
scale free networks according to their synchronizability in the limit.Comment: 7 pages, 2 figures, 1 tabl
Violation of hyperbolicity via unstable dimension variability in a chain with local hyperbolic chaotic attractors
We consider a chain of oscillators with hyperbolic chaos coupled via
diffusion. When the coupling is strong the chain is synchronized and
demonstrates hyperbolic chaos so that there is one positive Lyapunov exponent.
With the decay of the coupling the second and the third Lyapunov exponents
approach zero simultaneously. The second one becomes positive, while the third
one remains close to zero. Its finite-time numerical approximation fluctuates
changing the sign within a wide range of the coupling parameter. These
fluctuations arise due to the unstable dimension variability which is known to
be the source for non-hyperbolicity. We provide a detailed study of this
transition using the methods of Lyapunov analysis.Comment: 24 pages, 13 figure
Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks
Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete-time neural networks with time-varying delay. The individual neural network is subject to parameter uncertainty, stochastic disturbance, and time-varying delay, where the norm-bounded parameter uncertainties exist in both the state and weight matrices, the stochastic disturbance is in the form of a scalar Wiener process, and the time delay enters into the activation function. For the array of coupled neural networks, the constant coupling and delayed coupling are simultaneously considered. We aim to establish easy-to-verify conditions under which the addressed neural networks are synchronized. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally, robustly, exponentially synchronized in the mean square. The LMI-based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time-varying delay, and can be solved efficiently via the Matlab LMI Toolbox. Two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme
Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems
The existence of anticipatory, complete and lag synchronization in a single
system having two different time-delays, that is feedback delay and
coupling delay , is identified. The transition from anticipatory to
complete synchronization and from complete to lag synchronization as a function
of coupling delay with suitable stability condition is discussed. The
existence of anticipatory and lag synchronization is characterized both by the
minimum of similarity function and the transition from on-off intermittency to
periodic structure in laminar phase distribution.Comment: 14 Pages and 12 Figure
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