New finite-time synchronization analysis of a delayed memristive neurodynamic model

Dandan Ren,Aidi Yao

doi:10.1186/s13662-020-02929-x

Abstract

This paper presents theoretical results on the finite-time synchronization of delayed memristive neural networks (MNNs). Compared with existing ones on finite-time synchronization of discontinuous NNs, we directly regard the MNNs as a switching system, by introducing a novel analysis method, new synchronization criteria are established without employing differential inclusion theory and non-smooth finite time convergence theorem. Finally, we give a numerical example to support the effectiveness of the theoretical results.

Highlights

1 Introduction It is well known that Chua in [1] postulated the existence of the fourth circuit element in 1971, and he named this element memristor as a contraction of memory and resistor, Chua pointed out that the memristor can memorize its past dynamic history, such a memory characteristic makes it as a potential candidate for simulating biological synapses, and it has been shown that a simple memristive system can exhibit a plethora of complex dynamical behaviors
(2) Existing finite-time synchronization results on delayed memristive neural networks (MNNs) are mainly based on some generalized finite-time convergence theorem, in this paper, we study the finite-time synchronization without using them, the employed approach enriches the analysis method of MNNs
Different from the method employed in those works, in this paper, we directly study the finite-time synchronization of the delayed MNNs (2.1) without using the theory of differential equations with discontinuous right-hand sides

Summary

Introduction

It is well known that Chua in [1] postulated the existence of the fourth circuit element in 1971, and he named this element memristor as a contraction of memory and resistor, Chua pointed out that the memristor can memorize its past dynamic history, such a memory characteristic makes it as a potential candidate for simulating biological synapses, and it has been shown that a simple memristive system can exhibit a plethora of complex dynamical behaviors. (3) The theoretical results established in this paper are closely related to the location of the initial error states, which presents a new viewpoint of finite-time synchronization process. Proof of Theorem 3.1 For every solution ei(t) of error system (2.4), we treat it into two cases according to the location of initial error function: Case I: sup–θ≤s≤0(max1≤i≤n |ei(s)|) ≤ 1 In this case, we obtain from Lemma 3.3 that each error state component ei(t), i =. Different from the method employed in those works, in this paper, we directly study the finite-time synchronization of the delayed MNNs (2.1) without using the theory of differential equations with discontinuous right-hand sides. The theoretical results established in this paper enrich the already existing finite-time synchronization methods. We investigate the finite-time synchronization problem of the considered delayed system by some mathematical analysis techniques via constructing different Lyapunov functions.

Conclusion

Methods