Scaling-Base Drive Function Projective Synchronization between Different Fractional-Order Chaotic Systems

Ping Zhou,Kun Huang

doi:10.1155/2013/521812

Abstract

A new function projective synchronization scheme between different fractional-order chaotic systems, called scaling-base drive function projective synchronization (SBDFPS), is discussed. In this SBDFPS scheme, one fractional-order chaotic system is chosen as scaling drive system, one fractional-order chaotic system is chosen as base drive systems, and another fractional-order chaotic system is chosen as response system. The SBDFPS technique scheme is based on the stability theory of nonlinear fractional-order systems, and the synchronization technique is theoretically rigorous. Numerical experiments are presented and show the effectiveness of the SBDFPS scheme.

Highlights

In the past twenty years, many synchronization schemes for chaotic systems have been presented [1–9]
Consider the fractional-order scaling drive chaotic system and base drive chaotic system and one response chaotic system described by systems (2), (3), and (4), respectively as follows: Dqd[1] x1 = fd[1] (x1), (2)
By (10), the Scaling-Base Drive Function Projective Synchronization (SBDFPS) between the scaling drive system (2), base drive systems (3), and response system (4) is turned into the following problem: select suitable M1(x1, x2, y) ∈ Rn×n such that the system (10) asymptotically converges to zero

Summary

Introduction

In the past twenty years, many synchronization schemes for chaotic systems have been presented [1–9]. Motivated by the previous part, we demonstrated a new function projective synchronization scheme between different fractional-order chaotic systems in this paper, which is called scaling-base drive function projective synchronization (briefly denoted by SBDFPS). 2. The Scaling-Base Drive Function Projective Synchronization (SBDFPS) between Different Fractional-Order Chaotic Systems. Consider the fractional-order scaling drive chaotic system and base drive chaotic system and one response chaotic system described by systems (2), (3), and (4), respectively as follows: Dqd[1] x1 = fd[1] (x1) ,. By (10), the SBDFPS between the scaling drive system (2), base drive systems (3), and response system (4) is turned into the following problem: select suitable M1(x1, x2, y) ∈ Rn×n such that the system (10) asymptotically converges to zero.

Illustrative Examples

Conclusions