分数阶超混沌系统的线性广义同步观测器设计

首先利用分数阶的常微分动力系统的稳定性理论，通过判断线性化后平衡点的稳定不变特性、辅助以分岔图分析等数值手段，给出了新近提出的改进型超混沌L讧系统对应分数阶系统产生混沌现象的阶次参数范围；进一步，设计了一类广义线性同步观测器，该观测器的动力学行为能与原系统实现任意的线性关系的广义同步，而经典的完全同步、反相同步以及投影同步可以视为本文提出方法的特例．最后的数值仿真进一步证实了本文提出的观测器设计方案的有效性．

Linear generaized synchronization observer design of the fractional hyperchaotic system

Based on the stability theory of fractional ordinary differential equations,the fractional dynamics of the newly proposed Lü chaotic system was analyzed.The range of order parameter was given by judging the stability of the equilibrium of the locally linearized system and by using bifurcation graph analysis.Furthermore,a synchronization observer was designed for linear generalized synchronization of such a newly proposed nonlinear chaotic system,which has the dynamic behavior of realizing arbitrary linear generalized synchronization including classical complete synchronization,anti-synchronization,projective synchronization as special cases with the original system.Finally,the numerical simulation verifies our results.