Design of a four-wing heterogeneous fractional-order chaotic system and its circuit simulation

Abstract

Integer orders differential system is a special case of fractional-order differential system. Integer orders chaotic system that we usually study is ideally approximate to realistic chaotic system. Fractional-order chaotic system has broader and changeable values of order and more complex dynamical behavior than integer order chaotic system. Thus, fractional-order differential equation can describe the nonlinear characteristics of actual chaotic system more exactly, which has more prominent research meanings and application value. This paper designs a new four-wing four-dimensional heterogeneous fractional-order chaotic system, when the values of fractional-order qi (i = 1,2,3,4) i are not identical(q1=q2=0.9,q3=q4=0.8, in step size of 0.1), the attractors of this chaotic system will all show four-wing shapes in any direction. After analysis this chaotic system's stability and existence, this paper also introduces a nonlinear state feedback controller, and adopts the chain shape circuit to conduct experiment simulation through Multisim software 10.0. The results of circuit simulation and Matlab numerical operation have the same chaotic attractor phase diagram. This demonstrates the effectiveness of this four-wing four-dimensional heterogeneous fractional-order chaotic system's design and the feasibility of the feedback controller in the circuit; meanwhile, it provides referable bases for the application in actual circuits.