A New Hypersensitive Hyperchaotic System with No Equilibria

Abstract

In this paper, we propose a new four-dimensional hyperchaotic system derived from the chaotic maps of Peter de Jong’s simple attractor and the discrete iterative function. In this work, our main motivation is to explore a link that can be developed to generate hyperchaos from 2D chaotic system. An association between 2D system and a higher order one was not studied in the previous literature. In fact, in the literature, there is no two-dimensional systems from which we are able to associate a four-dimensional one. In this context, a special interest is reserved to Peter de Jong system due to its exceptional advantages such as hypersensitivity and velocity. The challenge in this paper is the development of a four-dimensional hyperchaotic system associated to the Peter de Jong one while conserving its important characteristics such as hypersensitivity, velocity and the lack of equilibrium. The system structure that we will detail is different from other hyperchaotic systems widely suggested in the literature. In fact, the proposed attractor does not display any equilibrium point. A mathematical study is carried out in order to obtain time plots, Lyapunov exponents spectrum and bifurcation diagram. Finally, we will prove the high sensitivity of this system relative to its initial condition by simulations and experimental observations.