Construction of multi-scroll chaotic attractors with exponential function

Abstract

Nonlinear function is the key to generating multi-scroll chaotic attractors. In view of this, a novel approach is presented generating multi-scroll chaotic attractors in this paper. By constructing a piecewise exponential function as the nonlinear term of Jerk system and expanding the function to multi-segment exponential function series, the index-2 equilibrium points of phase space of chaotic system are increased and different number of scroll chaotic attractors can be obtained. Some complex dynamical properties include phase diagram, equilibrium point, Lyapunov exponent spectrum, bifurcation diagram and Poincaré map are studied. The constructed function can be used in Chua system to generate multi-scroll attractors, which confirms the availability of this method.