In this paper we consider a new type of bifurcation to chaotic motion. This bifurcation is characterized by the simultaneous appearance of a pair of unstable fixed points or periodic orbits, a, fractal (i.e., nondifferentiable) basin boundary, and a chaotic attractor (also commonly called a strange attractor). Just prior to this type of bifurcation, transient behavior with a chaotic character c...

Abstract. In this paper, the linear feedback controlling of a novel chaotic system is discussed. The chaotic system is a new attractor which is similar to the Lorenz chaotic attractor, but it is not topological equivalent with the Lorenz chaotic system. This Letter proposes a novel approach for controlling this new attractor by linear feedback functions. The results obtained in this paper show ...

This paper proposes a novel four-dimensional autonomous system which has complex chaotic dynamics behaviors and gives analysis of novel system. More importantly, the novel system can generate three-layer chaotic attractor, four-layer chaotic attractor, five-layer chaotic attractor, multilayer chaotic attractor by choosing different parameters and initial condition. We analyze the new system by ...

Double crises of chaotic oscillators in the presence of fuzzy uncertainty are studied by means of the fuzzy generalized cellmappingmethod.A fuzzy chaotic attractor is characterized by its global topology and membership distribution. A fuzzy crisis implies a simultaneous sudden change both in the topology of the chaotic attractor and in its membership distribution. It happenswhen a fuzzy chaotic...

This letter investigates a new chaotic system and its role as a joint function between two complex chaotic systems, the Lorenz and the Chen systems, using a simple variable constant controller. With the gradual tuning of the controller, the controlled system evolves from the canonical Lorenz attractor to the Chen attractor through the new transition chaotic attractor. This evolving procedure re...

For a dynamical system described by a set of autonomous ordinary differential equations, an attractor can be a point, a periodic cycle, or even a strange attractor. Recently, a new chaotic system with only one stable equilibrium was described, which locally converges to the stable equilibrium but is globally chaotic. This paper further shows that for certain parameters, besides the point attrac...

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with onedimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space f...