Study of the dynamic properties of chaotic circuits in the presence of memristors

Abstract

This paper first discusses a memristor model based on a multi-segment linear function with three different circuits. Then, based on the different values of the parameters of the memristors introduced, the dynamic behavior of these circuits is analyzed in terms of bifurcations, coexisting attractors, and complexity. Bifurcation analysis reveals the rich dynamic behavior of these circuits, including period-doubling bifurcations, bursts of chaos, and transients of chaos. The Muthuswamy exhibit dynamic phenomena including coexisting attractors, multistability, and super multistability under different initial conditions. Moreover, circuit simulation is used to confirm the existence and feasibility of the Chua circuit. Coexisting attractor’s generation circuits that can alter the initial values of arbitrary state variables are designed. The advantages of the proposed system are illustrated by comparisons with other chaotic attractors, which include controllable attracter number and direction, straightforward implementation circuits, and rich dynamic behavior. Lastly, the Colpitts circuit, which contains the BTJ transistor and becomes steadier when a memristor is substituted for it, as well as the coexistence of multiple chaotic attractors, end up being more stable. Simulation results indicate that the three proposed circuit schemes in this paper require less time to achieve complete dynamics than other circuit schemes. This feature improves the suggested circuit strategy's effectiveness and usability in practical applications.