Dynamics, Circuit Design and Fractional-Order Form of a Modified Rucklidge Chaotic System

Abstract

Rucklidge chaotic system is a nonlinear mechanical model of a double convection process. In this paper, we modify the dynamics of a Rucklidge chaotic system by adding a nonlinear term and derive a new chaotic system. The nonlinear dynamics of the proposed chaotic system is described through numerical simulations which include the stability analysis of equilibrium points, phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and a Poincarè map. For specific values of the parameters, the proposed system displays periodic and chaotic behaviour. In addition, a new circuit implementation of the modified Rucklidge chaotic system is reported and examined in MultiSIM. A good qualitative agreement is shown between the simulations and the MultiSIM results. Furthermore, the fractional-order form of the modified Rucklidge chaotic system is numerically studied. By tuning the commensurate fractional order, the new chaotic system displays chaotic and periodic attractors, respectively.