一种新型双忆阻混沌系统动力学及其电路实现研究

在经典的蔡氏混沌电路基础上,引入三次非线性磁控忆阻模型,利用一个磁控忆阻模型和一个荷控忆阻模型,外加一个负电导替换变形蔡氏电路中的蔡氏二极管,设计了一个五阶混沌电路,用常规的方法研究系统的基本动力学特性。通过数值仿真结果表明电路在参数变化情况下能产生Hopf分岔和反倍周期分岔两种分岔行为,并能产生双涡卷、单涡卷、极限环、同宿轨等不同轨道,出现了双单摆运动。观察混沌吸引子推广到功率与能量信号,观察到蝴蝶翅膀重叠的奇异吸引子。通过改变初始值,能产生共存吸引子和周期极限环共存现象。为了验证电路的混沌行为,将对设计的电路进行了PSpice仿真,电路仿真结果验证了理论分析的正确性。

A Novel Dual Memristor Chaotic System Dynamics and Its Circuit Implementation

Based on the classic Chua’s chaotic circuit,by replacing Chua’s diode with negative conductance,we design a fifth-order chaotic circuit with memristors,which consists of a fiux-controlled memristor and a charge-controlled memristor. The fundamental dynamics of the system is studied by conventional methods. The analyses of equilibria and equilibrium stability show that the equilibrium stability is determined by the circuit parameters and the initial states of two memristors. The Lyapunov exponent spectra and bifurcation diagrams of the circuit imply that it can produce two bifurcation behaviors by adjusting its parameters,which are Hopf bifurcation and anti-period doubling bifurcation. The periodic orbits,double-scroll and single-scroll are found in the same system. Finally,the simulation results indicate that some strange attractors like Butterfly wing type exotic attractor are observed when voltage and electricity signal in observing chaotic attractors are generalized to power and energy signal,respectively. Specially,when different initial conditions of two memristors are used to simulate the circuit,we can find the coexistence phenomenon of chaotic attractors with different topological structures or quasi-periodic limit cycle and chaotic attractor. In order to ensure the occurrence of chaotic behaviors in the circuit,simulators of the charge-controlled memristor and the flux-controlled memristor are designed with conventional electronic devices,and PSpice simulation is conducted on the resulting circuit. PSpice simulation results verify the correctness of the theorectical analysis.