两类异质混沌系统的同步研究
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摘要
混沌系统的同步问题是非线性科学的研究热点问题之一.本文利用不连续动力系统理论研究了具有非线性控制约束的单摆系统与陀螺仪系统间的同步问题,给出了两个系统保持完全同步的条件,并通过建立同步开始或消失的转换条件,进一步讨论了两个系统的部分时间同步状态.最后通过数值模拟说明结论的有效性.
In this paper,the synchronization of two different chaotic systems is discussed by the theory of discontinuous dynamical system. The conditions for the full synchronization and partial synchronization are developed. At last, the effectiveness is illustrated by simulation.
In this paper,the synchronization of two different chaotic systems is discussed by the theory of discontinuous dynamical system. The conditions for the full synchronization and partial synchronization are developed. At last, the effectiveness is illustrated by simulation.
引文
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[12] 孙晓辉.一类异质二阶多自主体系统的一致性研究[J].山东师范大学学报:自然科学版,2015,30(3):1-5.
[2]Reggie B,Ljupco K. A unifying definition of synchronization for dynamical systems[J]. Chaos,2000, 10(2):344-349.
[3]Her-Terng Y. Generalized projective chaos synchronization of gyroscope systems subjected to dead-zone nonlinear inputs[J]. Physics Letters A,2008,372(14):2380-2385.
[4]Shi Y,Zhu P,Qin K. Projective synchronization of different chaotic neural networks with mixed time delays based on an integral sliding mode controller[J]. Neurocomputing,2014,123(123):443-449.
[5]Luo A C J. A theory for non-smooth dynamical systems on the connectable domains[J]. Communications in Nonlinear Science and Numerical Simulation, 2005,10(1):1-55.
[6]Luo A C J. Singularity and Dynamics on Discontinuous Vector Fields[M].Amsterdam:Elsevier,2006:28-30.
[7]Luo A C J. A theory for flow switchability in discontinuous dynamical systems[J]. Nonlinear Analysis: Hybrid Systems,2008,12(4):1030-1061.
[8]Luo A C J. Discontinuous Dynamical Systems on Time-Varying Domains[M]. Dordrecht: HEP-Springer,2009:115-118.
[9]Luo A C J, Min F H. Synchronization of a periodically forced, damped Duffing oscillator with a periodically excited pendulum[J]. Nonlinear Analysis: Real World Applications,2011,12(3):1810-1827.
[10] Min F,Luo A C J. Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints[J]. Chaos, Solitons and Fractals,2012,45(7):998-1011.
[11] Sun X,Fu X. Synchronization of two different dynamical systems under sinusoidal constraint[J]. Journal of Applied Mathematics,2014,31(6),1076-1101.
[12] 孙晓辉.一类异质二阶多自主体系统的一致性研究[J].山东师范大学学报:自然科学版,2015,30(3):1-5.