Search

In this paper, based on \mathbb CR calculus and penalty method, a one-layer recurrent neural network is proposed for solving constrained complex-variable convex optimization. It is proved that for any initial point from a given domain, the state of the proposed neural network reaches the feasible region in finite time and converges to an optimal solution of the constrained complex-variable convex optimization finally. In contrast to existing neural networks for complex-variable convex optimization, the proposed neural network has a lower model complexity and better convergence. Some numerical examples and application are presented to substantiate the effectiveness of the proposed neural network. [ABSTRACT FROM PUBLISHER]

This paper presents the multistability analysis of almost periodic state solutions for memristive Cohen–Grossberg neural networks (MCGNNs) with both distributed delay and discrete delay. The activation function of the considered MCGNNs is generalized to be nonmonotonic and nonpiecewise linear. It is shown that the MCGNNs with $n$ -neuron have $(K+1)^{n}$ locally exponentially stable almost periodic solutions, where nature number $K$ depends on the geometrical structure of the considered activation function. Compared with the previous related works, the number of almost periodic state solutions of the MCGNNs is extensively increased. The obtained conclusions in this paper are also capable of studying the multistability of equilibrium points or periodic solutions of the MCGNNs. Moreover, the enlarged attraction basins of attractors are estimated based on original partition. Some comparisons and convincing numerical examples are provided to substantiate the superiority and efficiency of obtained results. [ABSTRACT FROM AUTHOR]

We introduce a class of novel stochastic coupled systems in which the coupling structure is time-varying and the topology structure is not strongly connected, and first establish the system on a digraph with a time-varying weight matrix. Motivated by Du and Li (2014), we give a hierarchical method to deal with digraphs without strong connectivity and establish the corresponding hierarchical algorithm to realize this approach. Also, an example is given to illustrate our hierarchical algorithm and its feasibility. In the sequel, based on the theory of asymptotically autonomous systems, Kirchhoff’s matrix tree theorem, and Lyapunov method, several moment exponential stability criteria are presented, including a Lyapunov-type theorem and a coefficient-type criterion. Furthermore, theoretical results are applied to stochastic coupled oscillators with time-varying coupling structure (SCTCS), and the stability criterion of SCTCS is obtained. Finally, the effectiveness of theoretical results is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]