Abstract
Modified function projective synchronization via adaptive impulsive controller between two different financial hyperchaotic systems is investigated, where the external uncertainties are considered. The updated laws of the unknown parameters are given and the sufficient conditions are deduced based on Lyapunov stability theorem and the stability analysis of impulsive system. Finally, the two financial hyperchaotic systems are taken for example and the numerical examples are worked through for illustrating the main results.
Highlights
Chaos synchronization, an important topic in nonlinear science, has been developed and studied extensively in various fields including secure communication, biological systems, information science, chemical reactions, and plasma technologies [1,2,3]
Since Pecora and Carroll [4] introduced a method to synchronize two identical systems with different initial conditions, a variety of approaches have been proposed for the synchronization of chaotic systems including complete synchronization [5], phase synchronization [6], generalized synchronization [7], lag synchronization [8], exponential synchronization [9], projective synchronization [10, 11], modified function projective synchronization [12], and adaptive synchronization [13]
In recent years, function projective synchronization (FPS) of special form is introduced by some researches [14], where the drive system and response system could be synchronized up to a scaling function
Summary
An important topic in nonlinear science, has been developed and studied extensively in various fields including secure communication, biological systems, information science, chemical reactions, and plasma technologies [1,2,3]. Since Pecora and Carroll [4] introduced a method to synchronize two identical systems with different initial conditions, a variety of approaches have been proposed for the synchronization of chaotic systems including complete synchronization [5], phase synchronization [6], generalized synchronization [7], lag synchronization [8], exponential synchronization [9], projective synchronization [10, 11], modified function projective synchronization [12], and adaptive synchronization [13] Among those synchronization methods, in recent years, function projective synchronization (FPS) of special form is introduced by some researches [14], where the drive system and response system could be synchronized up to a scaling function. In this paper, we study its MFPS via an adaptive impulsive control method in this financial hyperchaotic system. By using the impulsive control method, the response system needs to receive the information from the drive system and achieve synchronization faster only at some discrete instants It has very strong advantage in practice.
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