中国物理B ›› 2011, Vol. 20 ›› Issue (12): 120508-120508.doi: 10.1088/1674-1056/20/12/120508

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Modified impulsive synchronization of fractional order hyperchaotic systems

马铁东1, 浮洁2, 余淼2   

  1. (1)College of Automation, Chongqing University, Chongqing 400044, China; (2)Key Laboratory of Optoelectronic Technology and System, Ministry of Education, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China
  • 收稿日期:2011-07-03 修回日期:2011-07-27 出版日期:2011-12-15 发布日期:2011-12-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 50830202 and 51073179), the Natural Science Foundation of Chongqing, China (Grant No. CSTC 2010BB2238), the Doctoral Program of Higher Education Foundation of Institutions of China (Grant Nos. 20090191110011 and 20100191120025), the Natural Science Foundation for Postdoctoral Scientists of China (Grant Nos. 20100470813 and 20100480043), and the Fundamental Research Funds for the Central Universities (Grant Nos. CDJZR11 12 00 03 and CDJZR11 12 88 01).

Modified impulsive synchronization of fractional order hyperchaotic systems

Fu Jie(浮洁)a)†, Yu Miao(余淼) a), and Ma Tie-Dong(马铁东)b)   

  1. a Key Laboratory of Optoelectronic Technology and System, Ministry of Education, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China; b College of Automation, Chongqing University, Chongqing 400044, China
  • Received:2011-07-03 Revised:2011-07-27 Online:2011-12-15 Published:2011-12-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 50830202 and 51073179), the Natural Science Foundation of Chongqing, China (Grant No. CSTC 2010BB2238), the Doctoral Program of Higher Education Foundation of Institutions of China (Grant Nos. 20090191110011 and 20100191120025), the Natural Science Foundation for Postdoctoral Scientists of China (Grant Nos. 20100470813 and 20100480043), and the Fundamental Research Funds for the Central Universities (Grant Nos. CDJZR11 12 00 03 and CDJZR11 12 88 01).

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摘要： In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.

关键词: hyperchaotic systems, fractional order chaotic systems, synchronization, impulsive control

Abstract: In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.

Key words: hyperchaotic systems, fractional order chaotic systems, synchronization, impulsive control

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Jn (High-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)