Fixed/Predefined-Time Synchronization of Complex-Valued Stochastic BAM Neural Networks with Stabilizing and Destabilizing Impulse

Abstract

This article is mainly concerned with the fixed-time and predefined-time synchronization problem for a type of complex-valued BAM neural networks with stochastic perturbations and impulse effect. First, some previous fixed-time stability results on nonlinear impulsive systems in which stabilizing and destabilizing impulses were separately analyzed are extended to a general case in which the stabilizing and destabilizing impulses can be handled simultaneously. Additionally, using the same logic, a new predefined-time stability lemma for stochastic nonlinear systems with a general impulsive effect is obtained by using the inequality technique. Then, based on these novel results, two novel controllers are implemented to derive some simple fixed/predefined-time synchronization criteria for the considered complex-valued impulsive BAM neural networks with stochastic perturbations using the non-separation method. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results.

Stochastic Synchronization of Impulsive Reaction–Diffusion BAM Neural Networks at a Fixed and Predetermined Time

“…The relevance of PDT synchronization in the mentioned systems was considered in Theorem 2, Corollary 3, and Corollary 4 of reference [33]. This simplification allows us to focus solely on the impulsive dynamics and the stochastic influences on the synchronization behavior.…”

“…Corollary 2. Suppose that Assumptions 1 and 2 are satisfied; then, the drive-response system in (32) and (33) exhibits PDT synchronization in probability under the controller in (7) if the control gains α i , β i , γ j and δ j satisfy the inequality k < min ψ, φ, − T c T 0 ln ζ ν τ .…”

“…Recently, finite-time (FNT) synchronization, both with and without reaction-diffusion, has gained attention among researchers [28][29][30][31]. FXT synchronization, which accomplishes synchronization in a fixed time, has become particularly popular [32,33]. In [32], the authors studied FXT synchronization for neural networks.…”

“…In [32], the authors studied FXT synchronization for neural networks. In another reference [33], FXT synchronization was successfully applied to impulsive neural networks with stochastic perturbations within a predefined time. The application of fixed-time synchronization in image encryption and machine learning can improve the security and stability of algorithms.…”

“…However, in FXT synchronization it is impossible to predict the convergence time. Researchers have made significant progress recently towards overcoming this limitation [33][34][35][36][37]. In [34], the authors proposed PDT synchronization for neural networks, which guarantees convergence of the error to zero within a specified time.…”