Pinning Impulsive Synchronization of Stochastic Delayed Neural Networks via Uniformly Stable Function

Synchronization in Coupled Neural Networks With Hybrid Delayed Impulses: Average Impulsive Delay-Gain Method

In this article, we propose a new concept called average impulsive delay-gain (AIDG) for studying the synchronization of coupled neural networks (CNNs). Based on the viewpoints of impulsive control and impulsive perturbation, we establish some globally exponential synchronization criteria for CNNs. Our methods are well-suited for addressing the synchronization problems of systems subject to hybrid delayed impulses with time-varying impulsive delay and gain. Moreover, we prove that the AIDG has both positive and negative effects on synchronization. Compared to existing research, our conclusions are more applicable and less conservative as the considered hybrid delayed impulses involve more flexible cases. Finally, we validate the effectiveness of our proposed results by applying them to small-world and scale-free network models.

Adaptive Drive-Response Synchronization of Timescale-Type Neural Networks With Unbounded Time-Varying Delays

In recent years, adaptive drive-response synchronization (DRS) of two continuous-time delayed neural networks (NNs) has been investigated extensively. For two timescale-type NNs (TNNs), how to develop adaptive synchronization control schemes and demonstrate rigorously is still an open problem. This article concentrates on adaptive control design for synchronization of TNNs with unbounded time-varying delays. First, timescale-type Barbalat lemma and novel timescale-type inequality techniques are first proposed, which provides us practical methods to investigate timescale-type nonlinear systems. Second, using timescale-type calculus, novel timescale-type inequality, and timescale-type Barbalat lemma, we demonstrate that global asymptotic synchronization can be achieved via adaptive control under algebraic and matrix inequality criteria even if the time-varying delays are unbounded and nondifferentiable. Adaptive DRS is discussed for TNNs, which implies our control schemes are suitable for continuous-time NNs, their discrete-time counterparts, and any combination of them. Finally, numerical examples on TNNs and timescale-type chaotic Ikeda-like oscillator with unbounded time-varying delays are carried out to verify the adaptive control schemes.

Aperiodic intermittent dynamic event-triggered synchronization control for stochastic delayed multi-links complex networks

In this work, the exponential synchronization issue of stochastic complex networks with time delays and time-varying multi-links (SCNTM) is discussed via a novel aperiodic intermittent dynamic event-triggered control (AIDE-TC). The AIDE-TC is designed by combining intermittent control with an exponential function and dynamic event-triggered control, aiming to minimize the number of the required triggers. Then, based on the proposed control strategy, the sufficient conditions for exponential synchronization in mean square of SCNTM are obtained by adopting graph theoretic approach and Lyapunov function method. In the meanwhile, it is proven that the Zeno behavior can be excluded under the AIDE-TC, which ensures the feasibility of the control mechanism to realize the synchronization of SCNTM. Finally, we provide a numerical simulation on islanded microgrid systems to validate the effectiveness of main results and the simulation comparison results show that the AIDE-TC can reduce the number of event triggers.

Periodicity and multi-periodicity generated by impulses control in delayed Cohen-Grossberg-type neural networks with discontinuous activations

This paper discusses the periodicity and multi-periodicity in delayed Cohen-Grossberg-type neural networks (CGNNs) possessing impulsive effects, whose activation functions possess discontinuities and are allowed to be unbounded or nonmonotonic. Based on differential inclusion and cone expansion-compression fixed-point theory of set-valued mapping, several improved criteria are given to derive the positive solution with ω-periodicity and ω-multi-periodicity for delayed CGNNs under impulsive control. These ω-periodicity/ω-multi-periodicity orbits are produced by impulses control. The analytical method and theoretical results presented in this paper are of certain significance to the design of neural network models or circuits possessing discontinuous neuron activation and impulsive effects in periodic environment.