Impulsive Synchronization and Adaptive-Impulsive Synchronization of a Novel Financial Hyperchaotic System

Abstract

The impulsive synchronization and adaptive-impulsive synchronization of a novel financial hyperchaotic system are investigated. Based on comparing principle for impulsive functional differential equations, several sufficient conditions for impulsive synchronization are derived, and the upper bounds of impulsive interval for stable synchronization are estimated. Furthermore, a nonlinear adaptive-impulsive control scheme is designed to synchronize the financial system using invariant principle of impulsive dynamical systems. Moreover, corresponding numerical simulations are presented to illustrate the effectiveness and feasibility of the proposed methods.

Mixed Synchronization of Chaotic Financial Systems by Using Linear Feedback Control

“…Theorem 1 gives a mixed synchronization criterion for chaotic financial systems (1) and (2). Compared with existing synchronization results in [19][20][21][22][23]25] for chaotic financial systems by using nonlinear feedback controls (the active control and adaptive control), the linear feedback control is used in Theorem 1.…”

“…In [19][20][21][22][23], hyperchaotic financial systems with four dimensions were studied. This paper mainly investigates the mix synchronization of three-dimensional chaotic financial systems (1).…”

“…The synchronization of two chaotic financial systems has been widely investigated in [19][20][21][22][23][24][25]. However, to the best of author's knowledge, there are limited studies to investigate the coexistence of synchronization and antisynchronization of two chaotic financial systems [26,27], in which the nonlinear control method (adaptive control) was used to achieve mixed synchronization.…”

“…However, to the best of author's knowledge, there are limited studies to investigate the coexistence of synchronization and antisynchronization of two chaotic financial systems [26,27], in which the nonlinear control method (adaptive control) was used to achieve mixed synchronization. Within those existing studies of synchronization (not mixed synchronization) of two chaotic financial systems, the nonlinear control methods (active control and adaptive control) were utilized in [19][20][21][22][23][24][25]. Therefore, we focus on using the linear feedback control to achieve the coexistence of synchronization and antisynchronization of two chaotic financial systems.…”

Bifurcation Analysis and Stability Criterion for the Nonlinear Fractional‐Order Three‐Dimensional Financial System with Delay

“…Financial and economic problems have been intensively studied in the past years as the impact of the economic crisis on human society has become more and more serious . A lack of control over the financial system will likely cause greater losses.…”