Initial conditions-related dynamical behaviors in PI-type memristor emulator-based canonical Chua’s circuit

Purpose The purpose of this paper is to construct a proportion-integral-type (PI-type) memristor, which is different from that of the previous memristor emulator, but the constructing memristive chaotic circuit possesses line equilibrium, leading to the emergence of the initial conditions-related dynamical behaviors. Design/methodology/approach This paper presents a PI-type memristor emulator-based canonical Chua’s chaotic circuit. With the established mathematical model, the stability region for the line equilibrium is derived, which mainly consists of stable and unstable regions, leading to the emergence of bi-stability because of the appearance of a memristor. Initial conditions-related dynamical behaviors are investigated by some numerically simulated methods, such as phase plane orbit, bifurcation diagram, Lyapunov exponent spectrum, basin of the attraction and 0-1 test. Additionally, PSIM circuit simulations are executed and the seized results validate complex dynamical behaviors in the proposed memristive circuit. Findings The system exhibits the bi-stability phenomenon and demonstrates complex initial conditions-related bifurcation behaviors with the variation of system parameters, which leads to the occurrence of the hyperchaos, chaos, quasi-periodic and period behaviors in the proposed circuit. Originality/value These memristor emulators are simple and easy to physically fabricate, which have been increasingly used for experimentally demonstrating some interesting and striking dynamical behaviors in the memristor-based circuits and systems.