Research on the Dynamics of Memristive Chaotic Systems via Nonlinear Feedback Control Inputs

The present paper proposes a novel four-dimensional memristive chaotic system, evolved from the simplest memristor chaotic circuit by integrating a second-order exponential internal state function and a quartic polynomial memristance model, along with nonlinear feedback control. The main feature of the new system is that it has infinitely many equilibrium points and an abundance of coexisting attractors and symmetries of their attractors. The dynamic properties of the system are quantitatively characterized through a multidimensional analysis that includes phase-space reconstruction, bifurcation mapping and Lyapunov exponent calculation. The accuracy and practical existence of the system are evaluated through the utilisation of analog circuits. Furthermore, the system is implemented through digital circuits that utilise the STM32 microcontroller. The system has passed the NIST tests, thereby demonstrating its potential in the domain of encryption applications. Theoretical analysis and simulation results indicate that the simple chaotic circuit has very rich dynamical characteristics.