Predefined-Time Antisynchronization of Two Different Chaotic Neural Networks

Abstract

This paper is concerned with antisynchronization in predefined time for two different chaotic neural networks. Firstly, a predefined-time stability theorem based on Lyapunov function is proposed. With the help of the definition of predefined time, it is convenient to establish a direct relationship between the tuning gain of the system and the fixed stabilization time. Then, the antisynchronization is achieved between two different chaotic neural networks via active control Lyapunov function design. The designed controller presents the practical advantage that the least upper bound for the settling time can be explicitly defined during the control design. With the help of the designed controller, the antisynchronization errors converge within a predefined-time period. Numerical simulations are presented in order to show the reliability of the proposed method.

A new judgment theorem for predefined‐time stability and its application in the synchronization analysis of neural networks

“…Remark In Reference 38, Lin proposed another judgment theorem for PDT stability. However, for this judgment theorem, even when the two sides of the Lyapunov‐like judging condition are equal, $$$ {\sup}_{\boldsymbol{z}(0)\in {\mathbb{R}}^n}T\left(\boldsymbol{z}(0)\right)={T}_p $$$ still does not hold.…”

“…However, the analysis techniques in References 28‐37 cannot be utilized to study the PDT synchronization of neural networks. In fact, the reported works about the PDT synchronization of neural networks are very few up to now 38,39 …”

“…In Reference 38, another judgment theorem for PDT stability was put forward, and it was used to study the PDT antisynchronization of chaotic neural networks. However, in practical applications, the required control gains based on the judgment theorem in Reference 38 will be too large. In References 23 and 27, another type of judgment theorem for PDT stability was reported.…”

Chaotic Honeybees Optimization Algorithms Approach for Traveling Salesperson Problem

“…Lin [53] proposed a predefined time stability theorem based on the Lyapunov function to facilitate the antisynchronization of the two CNNs. e engineered driver causes antisync errors to converge within a predefined period.…”

Predefined-Time Stability/Synchronization of Coupled Memristive Neural Networks With Multi-Links and Application in Secure Communication

“…Recently, Anguiano-Gijon et al (2019), Lin (2021b), Assali (2021), Lin et al (2021), andMuoz-Vazquez et al (2021) went further and discussed the predefined-time synchronization of two chaotic systems, one of them obtained the projective synchronization criterion about predefined-time (Lin et al, 2021), and another two of them considered chaotic systems of fractional-order forms (Lin et al, 2021;Muoz-Vazquez et al, 2021). In 2020, Lin defined the novel criterion of predefined-time synchronization in different kinds of neural networks, including a chaos neural network and memristive neural network (Lin et al, 2020;Lin, 2021a).…”