Antimonotonicity, Hysteresis and Coexisting Attractors in a Shinriki Circuit with a Physical Memristor as a Nonlinear Resistor

Abstract

A novel approach to the physical memristor’s behavior of the KNOWM is presented in this work. The KNOWM’s memristor’s intrinsic feature encourages its use as a nonlinear resistor in chaotic circuits. Furthermore, this memristor has been shown to act like a static nonlinear resistor under certain situations. Consequently, for the first time, the KNOWM memristor is used as a static nonlinear resistor in the well-known chaotic Shinriki oscillator. In order to examine the circuit’s dynamical behavior, a host of nonlinear simulation tools, such as phase portraits, bifurcation and continuation diagrams, as well as a maximal Lyapunov exponent diagram, are used. Interesting phenomena related to chaos theory are observed. More specifically, the entrance to chaotic behavior through the antimonotonicity phenomenon is observed. Furthermore, the hysteresis phenomenon, as well as the existence of coexisting attractors in regards to the initial conditions and the parameters of the system, are investigated. Moreover, the period-doubling route to chaos and crisis phenomena are observed too.

Keywords

• memristor
• chaos
• antimonotonicity
• hysteresis
• coexisting attractors
• nonlinear resistor