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.
Highlights
Since the seminal work of Pecora and Carroll [1], chaos synchronization has been an active topic in nonlinear science, due to its potential applications in secure communication, control theory, telecommunications, biological networks and artificial neural networks, and so forth
We investigated impulsive synchronization and adaptive-impulsive synchronization of a novel financial hyperchaotic system theoretically and numerically at the first time
We have proposed an impulsive synchronization scheme for the financial system, obtained some synchronization criteria by means of comparing system principle, estimated the upper bounds of impulsive interval for stable synchronization, and provided numerical simulation results to show the effectiveness of the synchronization criteria
Summary
Since the seminal work of Pecora and Carroll [1], chaos synchronization has been an active topic in nonlinear science, due to its potential applications in secure communication, control theory, telecommunications, biological networks and artificial neural networks, and so forth. In [18], Li et al discussed adaptive-impulsive synchronization and parameter identification of a class of chaotic and hyperchaotic systems, and their controllers and identifiers have a limit that the system state variable function independent of Mathematical Problems in Engineering parameters must be Lipchitz. We will design a nonlinear adaptive-impulsive control scheme to synchronize the financial system using invariant principle of impulsive dynamical systems.
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