Hyperchaos behaviors and chaos synchronization of two unidirectional coupled simplified Lorenz systems
来源期刊：中南大学学报(英文版)2014年第3期
论文作者：孙克辉 WANG Yan(汪艳) 王艳丽
文章页码：948 - 955
Key words：hyperchaos; chaos synchronization; coupling control; simplified Lorenz system
Abstract: To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincaré section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.
SUN Ke-hui(孙克辉)1, 2, WANG Yan(汪艳)1, WANG Yan-li(王艳丽)1
(1. School of Physics and Electronics, Central South University, Changsha 410083, China;
2. School of Physics Science and Technology, Xinjiang University, Urumqi 830046, China)
Abstract:To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincaré section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.
Key words:hyperchaos; chaos synchronization; coupling control; simplified Lorenz system
