Dynamical behaviors of a controllable memristive chaotic map

Abstract

Nonlinear characteristics of a nonlinear system can be enhanced by adding a memristor. A magnetic flux-controlled memristor is connected to one branch of a nonlinear circuit to estimate the effect of an external magnetic field. A charge-controlled memristor is applied to one branch of a nonlinear circuit to approach the effect of an external electric field. In this paper, a simple memristive circuit is designed by using a charge-controlled memristor, a nonlinear resistor and a capacitor, and this memristive circuit is controlled by applying an external signal source. And then an equation of a simple memristive circuit and its energy function are obtained based on Kirchhoff’s law and Helmholtz’s theorem. Furthermore, a memristive map is generated by using linear transformations for the variable in oscillator equations. The dynamical behaviors of a memristive map and its characteristics of an energy adaptive regulation are investigated. The results illustrate that the dynamical behavior of a memristive chaotic map can be controlled by adjusting external signal source and parameters, and the dynamical performance of the memristive map can also be controlled by applying energy controlled parameter adaptive growth method. This controlled memristive chaotic map can further be used in image encryption algorithm.