分数阶广义混沌系统分析及有限时间同步

Analysis of Fractional-order Generalized Chaotic Systems and Finite Time Synchronization

混沌是非线性动力系统中所特有的一种运动形式,将混沌系统抽象成数学模型并加以控制是探索混沌应用的主要形式,随着混沌系统研究的深入,分数阶系统逐渐从整数阶系统中脱颖而出,由此通过研究一类新的整数阶混沌系统,提出了相应的分数阶三维自治系统;通过系统的线性项判别,并根据分数阶Lyapunov稳定理论对于混沌系统中平衡点种类进行区分,发现该新分数阶系统产生的平衡点属于不稳定鞍点;对于该分数阶系统采用有限时间稳定理论,在驱动系统与响应系统中进行同步控制器的设计,通过数值仿真验证并绘制出有限时间同步关系曲线图验证了在短时间内实现混沌同步控制。

Chaos is a special form of motion in nonlinear dynamical system. It is the main form to explore the application of chaos in abstract chaotic system into mathematical model and to control it. With the deepening of chaotic system research,fractional order system gradually stands out from integer order system. By studying a new class of integer order chaotic systems,a fractional order 3 d autonomous system is proposed. According to Lyapunov stability theory,the equilibrium points in chaotic systems are distinguished by the linear terms of the system,and it is found that the equilibrium points generated by the new fractional-order system are unstable saddle points. For this fractional-order system,the finite-time stability theory is adopted to design the synchronization controller in the drive system and response system,and the finite-time synchronization relation graph is drawn through numerical simulation to verify the realization of chaotic synchronization control in a short time.