Strange Nonchaotic Attractors in Memristor-Based Shimizu–Morioka Oscillator

Abstract

The existence of strange nonchaotic attractors (SNAs) is examined using a memristor-based Shimizu–Morioka oscillator. In particular, we analyze the birth of SNAs by varying one of the frequency of external quasi-periodic forces. The occurrence and its mechanism are further analyzed through rational approximation theory. Following that, we also perform different nonlinear dynamical characterizations, including Poincaré surface sections, singular continuous spectrum, separation of nearby trajectories, 0–1 test, as well as finite-time Lyapunov exponents for more precise validation. Finally, the experimental evidence for the occurrence of SNA is inspected through a real-time analog circuit in the laboratory.