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Abstract: The dynamics of fractional-order systems have attracted increasing attentions in recent years. In this paper, the synchronization of two coupled nonlinear fractional order chaotic oscillators is numerically demonstrated using the master–slave synchronization scheme. It is shown that fractional-order chaotic oscillators can be synchronized with appropriate coupling strength. [Copyright &y& Elsevier]

Abstract: The stability of fuzzy large-scale systems with time delays both in states and in interconnections are considered in this paper. The fuzzy large-scale system consists of J interconnected subsystems, which are represented by the Takagi–Sugeno (T–S) fuzzy models. The stability conditions are derived using Lyapunov–Krasovskii approach, in combined with the linear matrix inequality (LMI) techniques. We also present a stabilization approach for the delayed fuzzy large-scale systems through fuzzy state feedback controllers. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. [Copyright &y& Elsevier]

Abstract: The occurrence of fractional-order chaotic dynamics have been intensively studied over the last ten years in a large number of real dynamical systems of physical nature. However, a similar study has not yet been carried out for fractional-order chaotic dynamical systems in the complex domain. In this paper, we numerically study the chaotic behaviors in the fractional-order symmetric and non-symmetric periodically forced complex Duffing’s oscillators. We find that chaotic behaviors exist in the fractional-order periodically forced complex Duffing’s oscillators with orders less than 4. Our results are validated by the existence of positive maximal Lyapunov exponent. [Copyright &y& Elsevier]

In this paper, based on the digital filter theory and approach, a new algorithm for training a complex-valued recurrent neural network, is proposed. Each recurrent neuron is modeled as an infinite impulse response (IIR) filter. The network weights are updated by optimizing the IIR filter coefficients, and the optimization is based on the layer-by-layer optimizing procedure as well as the recursive least-squares method. The performance of the proposed algorithm is demonstrated with application to a complex communication channel equalization. Our approach provides a new way to perform fast training of complex-valued recurrent neural networks.

In this paper, the bidirectional associative memory (BAM) neural network with axonal signal transmission delay is considered. This model is also referred to as a delayed dynamic BAM model. By combining a number of different Lyapunov functionals with the Razumikhin technique, some sufficient conditions for the existence of a unique equilibrium and global asymptotic stability of the network are derived. These results are fairly general and can be easily verified. Besides, the approach for the analysis allows one to consider several different types of activation functions, including piecewise linear sigmoids with bounded activations as well as C¹-smooth sigmoids. It is believed that these results are significant and convenient in the design and applications of BAM neural networks. Copyright © 2002 John Wiley & Sons, Ltd.

Bi-directional associative memory models are two-layer heteroassociative networks. In this paper, axonal signal transmission delay is introduced into BAM model yielding a class of generalized BAM networks. Conditions for the existence of equilibrium points, boundedness of trajectories and global stability are emphatically discussed for BAM with above-mentioned time delay. Circuit architecture of BAM with time delay is given. Correctness for our results is verified by using some examples and computer simulations. The obtained results have leading significance in the design and application of BAM networks. © 1998 John Wiley & Sons, Ltd.

Abstract: This paper presents fuzzy model-based designs for synchronization of hyperchaotic systems. The T–S fuzzy models for hyperchaotic systems are exactly derived. Based on the T–S fuzzy hyperchaotic models, the fuzzy controllers for hyperchaotic synchronization are designed via the exact linearization techniques. Numerical examples are given to demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

It is well known that complex dynamic behaviors exist in time-delayed neural systems. Infinite positive Lyapunov exponents can be found in time-delayed chaotic systems since the dimension of such systems is infinite. However, theoretical and experimental models studied thus far are low dimensional systems with only one positive Lyapunov exponent. Consequently, messages masked by such chaotic systems are shown to be easily extracted in some cases. Therefore, communication system with a higher security level can be design by means of the time-delayed neuron systems. In this paper, we firstly investigate the dynamical behaviors of two-neuron systems with discrete delays. Then, the chaos synchronization in time-delayed neuron system is studied based on the method of designing the coupled system and employing Krasovskii–Lyapunov theory to search the synchronization conditions. Numerical results illustrate the correctness of our theoretical analyses. [Copyright &y& Elsevier]

A simple model described by an autonomous continuous delayed differential equation with one variable, proposed by Uc¸ar, is considered in this paper. We will show that Hopf bifurcations occur in this simple system. The stability of bifurcating periodic solutions and the direction of Hopf bifurcations are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical analysis. [Copyright &y& Elsevier]

In this paper, we present a tabu search technique to approximately solve fuzzy optimization problems. We demonstrate the performance of the proposed method by applying it to an elementary fuzzy optimization problem. Other applications of the method to fuzzy linear programming, fuzzy regression and the training of fuzzy neural networks are also presented. [Copyright &y& Elsevier]

In this paper, we present a linear feedback controller design method for controlling chaotic Chua''s circuit based on piecewise quadratic Lyapunov functions. Firstly, we get the piecewise linear differential inclusions (pwLDIs) model of tracking error dynamics, then we design a linear state feedback controller to stabilize it based on the piecewise quadratic Laypunov functions. Finally, we give some numerical simulations to demonstrate the effectiveness of our theoretical results. [Copyright &y& Elsevier]

In recent years, backstepping method has been developed in the field of nonlinear control, such as controller, observer and output regulation. In this paper, an effective backstepping design is applied to chaos synchronization. There are some advantages in this method for synchronizing chaotic systems, such as (a) the synchronization error is exponential convergent; (b) only one variable information of the master system is needed; (c) it presents a systematic procedure for selecting a proper controller. Numerical simulations for the Chua's circuit and the Ro¨ssler system demonstrate that this method is very effective. [Copyright &y& Elsevier]

We consider an Internet model with a single link accessed by a single source, which responds to congestion signals from the network, and study bifurcation of such a system. By choosing the gain parameter as a bifurcation parameter, we prove that Hopf bifurcation occurs. The stability of bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical example is given to verify the theoretical analysis. [Copyright &y& Elsevier]