Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

Abstract

In this paper, we focus on synchronization issue of coupled multistable memristive neural networks (CMMNNs) with time delay under multiple stable equilibrium states. First, we build delayed CMMNNs consisting of one master subnetwork without controller and N − 1 identical slave subnetworks with controllers, and every subnetwork has n nodes. Moreover, this paper investigates multistability of delayed CMMNNs with continuous nonmonotonic piecewise linear activation function (PLAF) owning 2r + 2 corner points. By using the theorems of differential inclusion and fixed point, sufficient conditions are derived such that master subnetwork of CMMNNs can acquire (r + 2) n exponentially stable equilibrium points, stable periodic orbits or hybrid stable equilibrium states. Then, this paper proposes hybrid multisynchronization of delayed CMMNNs related with various external inputs under multiple stable equilibrium states for the first time. There exist (r + 2) n hybrid multisynchronization manifolds in CMMNNs with different initial conditions and external inputs. Finally, two numerical simulations are given to illustrate the effectiveness of the obtained results.

Chaos-Based Application of a Novel Multistable 5D Memristive Hyperchaotic System with Coexisting Multiple Attractors

“…A large number of new chaotic systems have been proposed one after another, and their application scopes are more and more extensive [1][2][3][4][5][6][7][8]. With the progress of science and technology, chaos has been applied not only to communication [9][10][11][12], image processing [13][14][15], complex networks [16][17][18][19][20][21], synchronization [22][23][24][25][26][27], electronic circuits [28][29][30], and optimization [31][32][33][34][35] but also to encryption studies [36][37][38][39][40][41]. is is because chaotic signal has good pseudorandom, initial-value sensitive, and long-term unpredictable characteristics, which enhances the confusion and diffusion of encrypted data.…”

Analysis and FPGA Realization of a Novel 5D Hyperchaotic Four‐Wing Memristive System, Active Control Synchronization, and Secure Communication Application

“…RK-4 is easier to implement than RK-5, so RK-4 is widely used to solve chaotic systems [103]. Equation (12) gives the formula for calculating K 1 , K 2 , K 3 , and K 4 , which represents the slope value of [y 0 , y i ]:…”

“…For the designed HFWMS, the initial conditions x(0) � 1, y(0) � − 1, z(0) � 1, w(0) � 1, and φ(0) � 1 and the step size h � 0.01 are given. Five equations in HFWMS are calculated according to the RK-4 algorithm flow chart and equation (12). By using the RK-4 algorithm of Verilog, the designed HFWMS is implemented on FPGA.…”

“…Nonlinear science is a new interdisciplinary subject to study the universality of nonlinear phenomena, which runs through almost every subject of meteorology [1,2], mathematics [3][4][5][6], uid mechanics [7,8], complex network [9][10][11][12], electronics [13][14][15], and social science [16,17]. Chaos is one of the most important achievements of nonlinear science.…”

CCII and FPGA Realization: A Multistable Modified Fourth-Order Autonomous Chua’s Chaotic System with Coexisting Multiple Attractors

“…Since 1960, the research and application of nonlinear systems have been more and more extensive. Many problems in complex networks [1][2][3][4][5][6][7], memristor [8][9][10][11], electronic circuits [12][13][14][15], image processing [16][17][18][19][20][21], economics [22], and other fields can be attributed to the study of nonlinear systems. Chaos is a special state of motion in a nonlinear system, which is a random-like behavior generated by a deterministic system and is extremely sensitive to initial values and highly dependent on them [23][24][25][26][27][28].…”