A new multi-wing chaotic attractor with unusual variation in the number of wings

Abstract

A new multi-wing chaotic system with some unusual properties is reported in this paper. Here, the number of wings and the amplitude of the chaotic attractor depend on (i) simulation time, (ii) initial conditions, and (iii) system parameters. The amplitude and number of wings of the multi-wing chaotic attractor are not reaching to a fixed chaotic attractor, as in the case of other chaotic systems like Lorenz, even after a very large simulation time of 800000 s. On the other hand, the Lyapunov exponents of the system remain the same with an increasing trend of the simulation time. Moreover, the amplitude and the number of wings of the chaotic attractor keep varying with the simulation time when the initial conditions and system parameters change. Such an unusual property of a chaotic attractor is termed as dynamic-chaotic attractor. In addition to these behaviors, different complex properties of this new chaotic system are explored by plotting phase portraits, Lyapunov spectrum, bifurcation diagrams and Poincare maps. Both homogeneous and heterogeneous multi-stability are found; the co-existence of 7 multi-wing chaotic attractors is reported. Hence, this kind of system is rare in the literature.