Nonlinear dynamics and hyperchaos in a modified memristor-based Chua's circuit and its generalized discrete system

Abstract

In this paper, a modified hyperchaotic memristor-based Chua's circuit and its generalized discrete model are reported. First, the dynamics of the continuous system are investigated using different tools, including stability theory, phase portraits, Lyapunov exponents, and bifurcation diagrams, showing that the proposed circuit model possesses a line of equilibrium and exhibits rich dynamics, including the coexistence of regular and chaotic attractors, and mixed-mode oscillations. Lastly, a generalized discrete version of the proposed system is formulated and its dynamics are explored. Using the Jury criterion, we constructed a useful stability test to localize some stable regions in three parameter planes. The presence of an exact periodic solution is numerically highlighted, and the occurrence of chaotic behavior is confirmed using the largest Lyapunov exponent and the 0−1 test.