A new fractional-order system displaying coexisting multiwing attractors; its synchronisation and circuit simulation

Abstract

Abstract This paper presents a novel chaotic system having tan-hyperbolic non-linearity exhibiting chaotic attractors with multiple wings (2 or more) in its fractional-order dynamics. Also, there is coexistence of these strange attractors which has been proved by continuation method. The proposed system displays two types of multistability, one on variation of initial conditions and other on keeping the initial condition constant but varying the offset variable. The dynamical analysis of the system is done by comparison between the theoretical calculations and validation of simulated results. Adaptive sliding mode controller is applied to the system with disturbance for synchronisation. Feasibility of circuit implementation is also shown for the fractional-order representation of the system and possibility coexistence of attractors in terms of different initial condition and offset variable by means of circuit simulation.