A Class of Different Fractional-Order Chaotic (Hyperchaotic) Complex Duffing-Van Der Pol Models and Their Circuits Implementations

Abstract

In this paper, we introduce three versions of fractional-order chaotic (or hyperchaotic) complex Duffing-van der Pol models. The dynamics of these models including their fixed points and their stability are investigated. Using the predictor-corrector method and Lyapunov exponents we calculate numerically the intervals of their parameters at which chaotic, hyperchaotic solutions and solutions that approach fixed points to exist. These models appear in several applications in physics and engineering, e.g., viscoelastic beam and electronic circuits. The electronic circuits of these models with different fractional-order are proposed. We determine the approximate transfer functions for novel values of fractional-order and find the equivalent tree shape model (TSM). This TSM is used to build circuits simulations of our models. A good agreement is found between both numerical and simulations results. Other circuits diagrams can be similarly designed for other fractional-order models.