Self-organizations with fast-slow time scale in a memristor-based Shinriki’s circuit

Abstract The structure of complex oscillations with two time scales generated by a novel memristor-based Shinriki’s circuit is studied in detail. Employing the stability phase diagrams, we identify the parameter regions of mixed-mode oscillations (MMOs) produced by each state variable, and classify the fast and slow properties of state variables according to the characteristics of these MMOs. Additionally, we exhibit the self-organizations of phases and describe how they are interconnected and how their complexity unfolds with control parameters varying. For several parameter combinations, in addition to recently reported shrimp-shaped cascades and “eye” of chaos, two kinds of interesting self-organizations, the shrimp cascade covered by four distinct numbers of peaks and “eye” of anti-chaos, are also discovered. A significant feature of these structures indicates that the fast-slow dynamics of the system depends not only on the state variables but also strongly on the parameter interval. The results of theoretical analyses obtained are verified by the Multisim simulation experiments. This paper will contribute to understanding the profound dynamical behaviors of the memristor-based circuit and open the possibility of studying hitherto unobserved phenomena.