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Dynamic Behaviors and the Equivalent Realization of a Novel Fractional-Order Memristor-Based Chaotic Circuit

机译:新型基于分数阶忆阻器的混沌电路的动力学行为和等效实现

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This paper proposed a novel fractional-order memristor-based chaotic circuit. A memristive diode bridge cascaded with a fractional-order RL filter constitutes the generalized fractional-order memristor. The mathematical model of the proposed fractional-order chaotic circuit is established by extending the nonlinear capacitor and inductor in the memristive chaotic circuit to the fractional order. Detailed theoretical analysis and numerical simulations are carried out on the dynamic behavior of the proposed circuit by investigating the stability of equilibrium points and the influence of circuit parameters on bifurcations. The results show that the order of the fractional-order circuit has a great influence on the dynamical behavior of the system. The system may exhibit complicated nonlinear dynamic behavior such as bifurcation and chaos with the change of the order. The equivalent circuits of the fractional-order inductor and capacitor are also given in the paper, and the parameters of the equivalent circuits are solved by an undetermined coefficient method. Circuit simulations of the equivalent fractional-order memristive chaotic circuit are carried out in order to validate the correctness of numerical simulations and the practicability of using the integer-order equivalent circuit to substitute the fractional-order element.
机译:本文提出了一种基于分数阶忆阻器的新型混沌电路。级联有分数阶RL滤波器的忆阻二极管桥构成了广义的分数阶忆阻器。通过将忆阻混沌电路中的非线性电容器和电感器扩展到分数阶,可以建立提出的分数阶混沌电路的数学模型。通过研究平衡点的稳定性以及电路参数对分叉的影响,对拟议电路的动态行为进行了详细的理论分析和数值模拟。结果表明,分数阶电路的阶数对系统的动力学行为有很大的影响。随着阶次的变化,系统可能表现出复杂的非线性动力学行为,例如分叉和混沌。文中还给出了分数阶电感器和电容器的等效电路,并通过不确定系数法求解了等效电路的参数。为了验证数值模拟的正确性和使用整数阶等效电路代替分数阶元素的实用性,对等效分数阶忆阻混沌电路进行了电路仿真。

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