A novel fractional nonautonomous system is proposed by introducing fractional order meminductor-memristor based circuit. Four circuit models are presented by different arrangements for the elements and the dynamic behaviors for each circuit are explored. It is observed that the four systems exhibit chaotic and hyperchaotic behaviors which have been verified using Lyapunov exponents. Bifurcation diagrams and phase portraits are employed to examine the effects of parameters variation on the qualitative dynamics of each model. An image encryption scheme is presented based on pseudo chaos orbit generated by two interval extensions of chaotic circuit model. The security analysis is carried out to verify the robustness and efficiency of the encryption scheme against possible attacks.

通过引入基于分数阶导磁-忆阻器的电路，提出了一种新颖的分数非自治系统。通过对元件的不同布置，提出了四个电路模型，并探索了每个电路的动态行为。可以观察到，这四个系统都表现出混沌和超混沌行为，这已经使用Lyapunov指数进行了验证。分叉图和相图用于检查参数变化对每个模型的定性动力学的影响。提出了一种基于混沌电路模型两次区间扩展生成的伪混沌轨道的图像加密方案。进行安全分析以验证加密方案的鲁棒性和效率，以防可能的攻击。