A New System with a Self-Excited Fully-Quadratic Strange Attractor and Its Twin Strange Repeller

Abstract

In nonlinear dynamics, the study of chaotic systems has attracted the attention of many researchers around the world due to the exciting and peculiar properties of such systems. In this regard, the present paper introduces a new system with a self-excited strange attractor and its twin strange repeller. The unique characteristic of the presented system is that the system variables are all in their quadratic forms; therefore, the proposed system is called a fully-quadratic system. This paper also elaborates on the study of the bifurcation diagram, the interpretation of Lyapunov exponents, the representation of basin of attraction, and the calculation of connecting curves as the employed method for investigating the system's dynamics. The investigation of 2D bifurcation diagrams and Lyapunov exponents indicated in this paper can better recognize the system's dynamics since they are plotted considering simultaneous changes of two parameters. Moreover, the connecting curves of the proposed system are calculated. The system's connecting curves help identify the system's different behaviors by providing general information about the nature of the flows.