Global Stability of Complex-Valued Recurrent Neural Networks With Time-Delays

Abstract

Since the last decade, several complex-valued neural networks have been developed and applied in various research areas. As an extension of real-valued recurrent neural networks, complex-valued recurrent neural networks use complex-valued states, connection weights, or activation functions with much more complicated properties than real-valued ones. This paper presents several sufficient conditions derived to ascertain the existence of unique equilibrium, global asymptotic stability, and global exponential stability of delayed complex-valued recurrent neural networks with two classes of complex-valued activation functions. Simulation results of three numerical examples are also delineated to substantiate the effectiveness of the theoretical results.

Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

“…The choice of the activation function is the main challenge in the dynamical behavior analysis of complexvalued neural networks compared to the study of real-valued neural networks. The complex-valued activation functions were supposed to need explicit separation into a real part and an imaginary part in [3,5,[8][9][10]18]. However, this separation is not always expressible in an analytical form.…”

“…Although there have been various methods for studying the diverse complex-valued neural networks, the scalar Lyapunov function method combined with the LMI method is nearly the most popular method to research the stability problem and synchronization problem (see [3,4,11,13,20,29,33]). The continuously distributed delays were not considered in the mentioned references.…”

“…Separating the model of complex-valued neural networks into its real and imaginary parts is a routine method (e.g., [3,[8][9][10]18]). The complex-valued activation functions were supposed to be with existence, continuity, and boundedness of the partial derivatives of the activation functions about the real and imaginary parts of the state variables, which impose restrictions on the applications of the obtained results.…”

“…As a very important issue, dynamical behavior analysis including existence, uniqueness, and stability of the equilibrium point of neural networks has attracted growing interest in the past decades (see [3][4][5][6][7][8][9][10][11] and the references therein). Different stability concepts as an important topic were defined in the existing references, such as exponential stability [2,7,12,13], robust stability [14,15], complete stability [16], multistability [17,18], Lagrange stability [19,20], and asymptotic stability [21].…”

Target Recognition Based on Rough Set with Multi-Source Information

“…In essence, identification with multi-attribute means the process of integrating multi-source information. In the field of target recognition technology, the main mathematical analysis methods include The Bayes estimation [1], DS evidence theory [2], fuzzy set theory [3][4][5][6][7][8], neural networks [9][10][11][12][13][14][15], artificial intelligence technology [16], rough set theory [17][18][19][20][21], and so on.…”