Synchronization in an array of linearly stochastically coupled networks with time delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2007 Elsevier LtdIn this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.This work was jointly supported by the National Natural Science Foundation of China under Grant 60574043, the Royal Society of the United Kingdom, the Natural Science Foundation of Jiangsu Province of China under Grant BK2006093, and International Joint Project funded by NSFC and the Royal Society of the United Kingdom

Synchronization of coupled neural oscillators with heterogeneous delays

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.Comment: 18 pages, 14 figure

Multiobjective synchronization of coupled systems

Copyright @ 2011 American Institute of PhysicsSynchronization of coupled chaotic systems has been a subject of great interest and importance, in theory but also various fields of application, such as secure communication and neuroscience. Recently, based on stability theory, synchronization of coupled chaotic systems by designing appropriate coupling has been widely investigated. However, almost all the available results have been focusing on ensuring the synchronization of coupled chaotic systems with as small coupling strengths as possible. In this contribution, we study multiobjective synchronization of coupled chaotic systems by considering two objectives in parallel, i. e., minimizing optimization of coupling strength and convergence speed. The coupling form and coupling strength are optimized by an improved multiobjective evolutionary approach. The constraints on the coupling form are also investigated by formulating the problem into a multiobjective constraint problem. We find that the proposed evolutionary method can outperform conventional adaptive strategy in several respects. The results presented in this paper can be extended into nonlinear time-series analysis, synchronization of complex networks and have various applications

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks

Controller design for synchronization of an array of delayed neural networks using a controllable

This is the post-print version of the Article - Copyright @ 2011 ElsevierIn this paper, a controllable probabilistic particle swarm optimization (CPPSO) algorithm is introduced based on Bernoulli stochastic variables and a competitive penalized method. The CPPSO algorithm is proposed to solve optimization problems and is then applied to design the memoryless feedback controller, which is used in the synchronization of an array of delayed neural networks (DNNs). The learning strategies occur in a random way governed by Bernoulli stochastic variables. The expectations of Bernoulli stochastic variables are automatically updated by the search environment. The proposed method not only keeps the diversity of the swarm, but also maintains the rapid convergence of the CPPSO algorithm according to the competitive penalized mechanism. In addition, the convergence rate is improved because the inertia weight of each particle is automatically computed according to the feedback of fitness value. The efficiency of the proposed CPPSO algorithm is demonstrated by comparing it with some well-known PSO algorithms on benchmark test functions with and without rotations. In the end, the proposed CPPSO algorithm is used to design the controller for the synchronization of an array of continuous-time delayed neural networks.This research was partially supported by the National Natural Science Foundation of PR China (Grant No 60874113), the Research Fund for the Doctoral Program of Higher Education (Grant No 200802550007), the Key Creative Project of Shanghai Education Community (Grant No 09ZZ66), the Key Foundation Project of Shanghai(Grant No 09JC1400700), the Engineering and Physical Sciences Research Council EPSRC of the U.K. under Grant No. GR/S27658/01, an International Joint Project sponsored by the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Complex partial synchronization patterns in networks of delay-coupled neurons

We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

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

Multiple chaotic central pattern generators with learning for legged locomotion and malfunction compensation

An originally chaotic system can be controlled into various periodic dynamics. When it is implemented into a legged robot's locomotion control as a central pattern generator (CPG), sophisticated gait patterns arise so that the robot can perform various walking behaviors. However, such a single chaotic CPG controller has difficulties dealing with leg malfunction. Specifically, in the scenarios presented here, its movement permanently deviates from the desired trajectory. To address this problem, we extend the single chaotic CPG to multiple CPGs with learning. The learning mechanism is based on a simulated annealing algorithm. In a normal situation, the CPGs synchronize and their dynamics are identical. With leg malfunction or disability, the CPGs lose synchronization leading to independent dynamics. In this case, the learning mechanism is applied to automatically adjust the remaining legs' oscillation frequencies so that the robot adapts its locomotion to deal with the malfunction. As a consequence, the trajectory produced by the multiple chaotic CPGs resembles the original trajectory far better than the one produced by only a single CPG. The performance of the system is evaluated first in a physical simulation of a quadruped as well as a hexapod robot and finally in a real six-legged walking machine called AMOSII. The experimental results presented here reveal that using multiple CPGs with learning is an effective approach for adaptive locomotion generation where, for instance, different body parts have to perform independent movements for malfunction compensation.Comment: 48 pages, 16 figures, Information Sciences 201