Hidden attractors in a class of two-dimensional rational memristive maps with no fixed points

Abstract

This paper reports a class of two-dimensional rational memristive maps by introducing a general discrete memristor model into the two-dimensional rational maps. Interestingly, there are no fixed points in the rational memristive maps. So all the attractors in the rational memristive maps are hidden, which has been rarely found in memristive maps. We take the quadratic memristor as an example. The complex dynamical behaviors of the two-dimensional rational maps with the quadratic memristor are studied by utilizing numerical tools, including phase portrait, basin of attraction, bifurcation diagram and Lyapunov exponents. Based on our investigation, these maps can generate different types of solutions, such as periodic, chaotic, quasi-periodic and hyper-chaotic solutions. In addition, the coexistence of hidden attractors can also be observed.