Improved Chaotic Dynamics of a Fractional-Order System, its Chaos-Suppressed Synchronisation and Circuit Implementation

Abstract

This paper presents (1) a new and improved fractional-order chaotic system (FOCS); (2) design of controllers for suppression of chaos for commensurate and incommensurate orders in the regions: $$0<\alpha \le 1$$0<?≤1 and $$1<\alpha <2$$1<?<2; (3) synchronisation between the new FOCS (as master) and a non-identical FOCS (as slave) when the master is in either chaotic mode or chaos-suppressed mode and finally (4) analog circuit implementation to validate the numerical simulation results. The rich variety of complex nonlinear dynamical behaviour is explored by varying the parameters as well as the fractional orders. Effective control strategies are designed to suppress chaos in the new system. In addition to this, the paper contributes the idea of synchronisation of the FOCS when it switches between chaotic and chaos-suppressed mode. The control scheme put forward in the paper is able to synchronise the slave with the switching master effectively in spite of change in dynamics. The paper compares the improved features of the newly proposed FO model with a class of well-known FOCSs and elaborates its capability to enhance the performance of secure communication. Circuit implementation results for all the above are in perfect agreement with those obtained through theoretical analyses and numerical simulations and thus reveal that the objectives of the paper are successfully achieved.