分数阶Genesio Tesi系统的混沌及自适应同步

对具有五次方非线性项的分数阶Genesio-Tesi系统的混沌及自适应同步进行了研究.首先分析了该系统平衡点的稳定性,并发现该系统满足出现双涡卷混沌吸引子的必要条件.然后研究了在阶数相同和不同的两种情况下的吸引子以及系统随阶数变化的分岔情况.该系统在两种情况下存在混沌的最小有效维数分别为2.784和2.793.基于分数阶系统的稳定性理论,实现了该分数阶系统的自适应混沌同步.数值模拟验证了所设计的自适应控制器和未知参数的辨识观测器的有效性.

Chaos and adaptive synchronization in fractional order Genesio Tese systems

The chaos and adaptive synchronization for a fractional order Genesio Tesi system with fifth order nonlinearity were investigated. The stability of equilibrium points was studied, and the necessary condition for double scroll attractor existence in the system was satisfied. The bifurcation and an interior crisis from single scroll to double scroll attractors were also found with the variation of derivative order. The minimum effective dimension for the system to remain chaos is 2.784 in commensurate order case and 2.793 in incommensurate order case. Furthermore, the adaptive synchronization of the system with uncertain parameters via back stepping approach was realized by designing appropriated controllers. Numerical simulations were carried out to demonstrate the effectiveness and flexibility for the controllers.