Controlling a 4D Chaotic Oscillator with a Quadratic Memductance and its Implementation

Abstract

Following the experimental realization of memristors, researchers have focused on memristor-based circuits. Chaotic circuits can be implemented easily using a memristor due to its nonvolatile and nonlinear behavior. This study presents a memristor-based four-dimensional (4D) chaotic oscillator with a line equilibria. A memristor having quadratic memductance was utilized to implement the proposed chaotic oscillator. The 4D chaotic oscillator with quartic nonlinearity was designed as a result of the quadratic memductance. In terms of communication security, random number generation and image and audio encryption, systems with quartic nonlinearity or that are higher-dimensional are better than systems that are lower-dimensional or possess quadratic/cubic nonlinearity. The performance of the proposed chaotic circuit was investigated according to properties such as phase portraits, Jacobian matrices, equilibrium points, Lyapunov exponents and bifurcation analyses. Furthermore, the proposed system is multistable and its solutions tend to appear as twin attractors when initial conditions approach their equilibria. The Lyapunov-based nonlinear controller was constructed for controlling the proposed system having a line equilibria. The effect of the initial conditions on the controlling indicators was also studied. In conclusion, by using discrete circuit elements, the proposed circuit was constructed, and its experimental results demonstrated a good agreement with the simulation results.