基于分数阶忆阻器的混沌电路分析与设计

Analysis and design of chaotic circuit based on fractional-order memristor

提出了一种新型的分数阶忆阻混沌电路。首先,建立了分数阶忆阻器的数学模型,通过数值仿真验证了分数阶广义忆阻器满足忆阻器的基本特性。然后,将分数阶广义忆阻器与蔡氏振荡电路相结合,建立了一种基于分数阶广义忆阻器的混沌电路模型。通过稳定性理论,对分数阶系统的稳定性进行了分析。为了进一步研究电路参数对系统动态行为的影响,利用相位图和分岔图等分析了系统随参数变化的动力学特性。结果表明,分数阶忆阻混沌电路会表现出周期和混沌等不同的动力学行为。最后,设计了分数阶忆阻混沌电路的等效电路模型,并进行电路仿真验证。实验结果与数值仿真结果基本一致,表明分数阶忆阻混沌电路具有一定的实际应用价值。

A novel chaotic circuit was proposed using fractional-order memristor.Firstly,a mathematical model of the fractional-order memristor was established.Through numerical simulation,it verified that the fractional-order memristor satisfied all fundamental characteristics of memristors.Secondly,by simultaneously using the fractional-order memristor and Chua's oscillator circuit,a chaotic circuit model was established.The fractional-order system was then analyzed by stability theory.To study the effect of circuit parameters on the dynamic behavior of the system,the dynamic characteristics of the system were analyzed by using phase trajectory diagram and bifurcation diagram during varying the circuit parameters.The results show that the fractional-order memristive chaotic circuit can exhibit different dynamic behaviors such as periodic state and chaotic state.Finally,the equivalent circuit model of the fractional-order memristor-based chaotic circuit was designed and verified by circuit simulation.The experimental results basically verified the numerical simulation.It means that the fractional-order memristor-based chaotic circuit has certain practical application value.