Coexistence of multi-scroll chaotic attractors for a three-dimensional quadratic autonomous fractional system with non-local and non-singular kernel

Abstract

In this paper, we present a numerical scheme and mathematical analysis for the famous three-dimensional quadratic autonomous self-govern system that happens to be chaotic with the coexistence of multi-scroll attractors. The scheme is based on the Atangana-Baleanu fractional derivative in the Caputo sense. The formulation of these schemes introduces the non-local and non-singular kernel to the fractional derivatives. The fractional derivative is then approximated using the family of the Adams–Bashforth schemes. The results are presented in both numerical and graphical as the fractional order β varies between 0<β⩽1. We study the proposed model in the both generalized case that is 0<β<1 and the case where β=1, which is the integer standard case. Due to the impact of the generalized case, the proposed model is able to maintain the coexistence of multi-scroll attractors.

Keywords

• Fractional derivative model
• Adams–Bashforth method
• Three-dimensional autonomous system
• Multi-scroll chaotic attractor
• Stability analysis
• Residual analysis