Chaos in the discrete memristor-based system with fractional-order difference

The mathematical modeling of memristor in discrete-time domain is an attractive new issue, but there are still some problems to be explored. This paper studies an interesting second-order memristor-based map model, and the model is constructed to three systems based on Caputo fractional-order difference. Their dynamic behaviors are investigated by the volt-ampere curve, bifurcation diagram, maximum Lyapunov exponent, attractor phase diagram, complexity analysis and basin of attraction. Numerical simulation analysis shows that the fractional-order system exhibits quasi periodic, chaos, coexisting attractors and other complex behaviors, which demonstrates more abundant dynamic behaviors of the fractional-order form. It lays a good foundation for the future analysis or engineering application of the discrete memristor.

Automated summary

This paper investigates an interesting second-order memristor-based map model using Caputo fractional-order difference, and explores its dynamic behaviors through various analysis methods. The numerical simulations show that the fractional-order system exhibits a range of complex behaviors, laying a solid foundation for future analysis and engineering applications of discrete memristors.