Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays

Chaos: An Interdisciplinary Journal of Nonlinear Science

Fang

2009

Self Cite

129

In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The well-studied integer-order complex networks are the special cases of the fractional-order ones. The network model considered can represent both directed and undirected weighted networks. First, based on the eigenvalue analysis and fractional-order stability theory, some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated. A surprising finding is that the fractional-order complex networks can stabilize itself by reducing the fractional-order q without pinning any node. Second, numerical algorithms for fractional-order complex networks are introduced in detail. Finally, numerical simulations in scale-free complex networks are provided to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter ␤, the larger overall coupling strength c, the more capacity that the pinning scheme may possess to enhance the control performance of fractional-order complex networks. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3068350͔Recently, fractional-order differential systems have been widely investigated due to their potential applications in viscoelasticity, dielectric polarization, quantum evolution of complex systems, and many other fields. On the other hand, research of complex networks has triggered tremendous interest during the past decade. Most studies to date have concerned integer-order complex networks. In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The fractional-order complex networks generalize wellstudied integer-order complex networks. Some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated by utilizing the eigenvalue analysis and fractional-order stability theory. A surprising finding that the fractional-order networks can stabilize itself by reducing the fractional-order q without pinning any node is presented. The numerical algorithms for fractional-order networks are also presented. In the end, computer simulations in scale-free networks are given to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter ␤, the larger coupling strength c, the more capacity that the pinning strategy can possess to accelerate the control rate of fractional-order networks.

Section: Introductionmentioning

confidence: 99%

Pinning control of fractional-order weighted complex networks

Chaos: An Interdisciplinary Journal of Nonlinear Science

Fang

2009

Self Cite

129

“…6(b) and Fig. 6(c) that the error states of synchronization tend to zero faster and more accurate than the conventional adaptive method in [25,26], which demonstrates the great efficiency of CPPSO presented in this paper.…”

Section: Remarkmentioning

confidence: 60%

“…Recently, synchronization problems of an array of continuous-time delayed neural networks have been investigated extensively in [4,5,15,25,26,38]. The controller designed in above works are used in terms of LMIs or adaptive controller.…”

Section: Remarkmentioning

confidence: 99%

“…For instance, the synchronization hypothesis for brain activities was formulated in 1938 [35], and the modern neurophysiological experiments reinforced that synchronous oscillations of neural activities in the brain structures are important in signal processing and coding [10]. For details concerning synchronization of neural networks, we refer the authors to see [4,5,13,15,25,26,38], and the references cited therein. However, in these well-studied works, linear matrix inequality (LMI) and adaptive method are employed to synchronize an array of neural networks, where a number of assumptions are needed for mathematical derivation and the results obtained have conservativeness.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Fang

2011

Information Sciences

Self Cite

This paper introduces a controllable probabilistic particle swarm optimization (CPPSO) algorithm based on Bernoulli stochastic variables and a competitive penalized method. The CPPSO is proposed to solve optimization problems and is applied to design the memoryless feedback controller, which is used in synchronization of an array of delayed neural networks (DNNs). The learning strategies occur in a random way and are governed by Bernoulli stochastic variables. The expectation of Bernoulli stochastic variables are automatically controlled by search environment. The proposed method not only keeps the diversity of the swarm, but also maintains rapid convergence of the PSO according to a competitive penalized mechanism. In addition, the convergence speed is improved because the inertia weight each particle is automatically computed according to the feedback of fitness value. The efficiency of the proposed CPPSO is demonstrated by comparing it with some well-known PSO algorithms on benchmark test functions with and without rotation. In the end, the proposed CPPSO algorithm is used to design the controller for synchronization of an array of continuous-time delayed neural networks.

“…13,14 One of the most intuitive approach dealing with synchronization of coupled chaotic systems is to use adaptive evolving coupling, which is based on feedback information and observed in many real-world networks. [15][16][17][18][19][20] Although the importance of synchronization has been widely recognized, almost all available results have been focusing on ensuring the synchronization of coupled chaotic systems with as small coupling strengths as possible. In reality, however, the choice of coupling strengths actually affects the convergence rate and the coupling strengths which can be used to measure the synchronization performance or synchronization cost.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective synchronization of coupled systems

Chaos: An Interdisciplinary Journal of Nonlinear Science

Wong

et al. 2011

Self Cite

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