Hidden attractors without equilibrium and adaptive reduced-order function projective synchronization from hyperchaotic Rikitake system
Hidden attractors without equilibrium and adaptive reduced-order function projective synchronization from hyperchaotic Rikitake system
复制标题
超混沌 Rikitake 系统中无平衡的隐藏吸引子和自适应降阶函数投影同步
DOI：
10.1007/s12043-017-1363-6
复制
发表时间：
2017-04-01
影响因子：
2.8
通讯作者：
Pan, Weiquan
中科院分区：
文献类型：
--
作者：
Feng, Yu;Pan, Weiquan
通过在经典Rikitake系统中引入附加状态反馈，得到了一种新的非平衡态超混沌系统。通过数值模拟和分析，包括时间相图、Lyapunov指数和Poincaré映射对所提出的系统进行了研究。基于自适应控制和Lyapunov稳定性理论，设计了一种降阶投影同步方案，实现了无平衡点共存的超混沌Rikitake系统与两个非双曲平衡点共存的经典Rikitake系统的同步。最后，通过数值仿真验证了该同步方案的有效性。
By introducing an additional state feedback into classic Rikitake system, a new hyperchaotic system without equilibrium is derived. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincaré maps. Based on adaptive control and Lyapunov stability theory, we design a reduced-order projective synchronization scheme for synchronizing the hyperchaotic Rikitake system coexisting without equilibria and the original classic Rikitake system coexisting with two non-hyperbolic equilibria. Finally, numerical simulations are given to illustrate the effectiveness of the proposed synchronization scheme.