A new four-dimensional system containing chaotic or hyper-chaotic attractors with no equilibrium, a line of equilibria and unstable equilibria

Abstract

In this paper, a new multi-character dynamical system is proposed. It has chaotic and hyper-chaotic attractors without any equilibrium, with a line of equilibria or with unstable equilibrium. It means that the proposed system can change its characteristic by varying its parameters. This system shows multi-stability between different attractors such as quasi-periodic and chaotic attractors, quasi-periodic and periodic attractors, two periodic attractors and also two chaotic attractors.