Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks

Abstract

We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

Chaos Synchronization of Financial Chaotic System with External Perturbation

“…Theorem 11. System (1) and system (4) are asymptotically synchronized with the following adaptive control mechanism:…”

“…In nonlinear areas, researchers are striving to utilize the theory of nonlinear dynamics, especially the chaos theory, to study the complexity of economic and financial systems in recent years [1][2][3][4][5][6]. Since Strotz et al have done the pioneering work in this area [7], various economics chaotic models have been proposed, such as the Kaldorian model [8], the IS-LM model [9][10][11], the hyperchaotic finance system [12], and other nonlinear dynamical models [13][14][15][16].…”

Synchronization and Antisynchronization of Identical 4D Hyperchaotic Financial System with External Perturbation via Sliding Mode Control Technique

“…In recent years, financial chaotic systems have been widely investigated due to their globally socioeconomically importance. Researchers are still exploring the new dimensions regarding synchronization and antisynchronization of financial chaotic systems, which is also considered an attractive idea of this era [27][28][29][30]. Since the fundamental chaotic financial models proposed in the literature from [31][32][33][34][35][36][37], like the Kaldorian model is listed at [31] and the IS-LM model as [32,33], the hyperchaotic financial model is considered as [34]; moreover, the other nonlinear dynamical models are cited at [35][36][37].…”