Segmented disc dynamo with symmetric multidirectional patterns of multiscroll chaotic attractors

Abstract

Rather than adopting the common approach that the multiscroll attractors are obtained through reconstruction of nonlinear functions, this work presents a systematic mechanism for designing multidirectional symmetric multiscroll patterns of chaotic attractors. The present scheme is based on the multilevel signal that work with the nonlinearities and state variables of chaotic system to generate symmetric multidirectional patterns of multiscroll chaotic attractors (MPMCA). To illustrate the mechanism of this systematic approach, the coefficients of quadratic terms of segmented disc dynamo are modified and designed a chaotic system that generates a chaotic attractor consisting of two pairs of symmetrical attractors. The state variables under the multilevel signal are transformed and then combined the symmetric attractors to generate a complete family of symmetric MPMCA in multi directions (including one directional (1D), two directional (2D) and three directional (3D) symmetric patterns of multiscroll chaotic attractors). Chaotic dynamical characteristics of symmetric MPMCA are analysed​ by means of equilibrium points distribution and phase portraits. Matlab simulations results obtained in this work are consistent well with our theoretical analysis verifying the effectiveness of the presented scheme.