Two fractional chaotic maps, Lu and Chen have been analyzed using an innovative predictor-corrector method based on a non-uniform grid. An original law to control the grid size at each iteration has introduced. The choice of was shown play fundamental role obtain behavior for larger parameter range, while decreasing computational time. obtained results show that complexity resulting system in t...

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...

This research work describes a nine-term 3-D novel chaotic system with four quadratic nonlinearities. First, this work describes the dynamic analysis of the novel chaotic system and qualitative properties of the novel chaotic system are derived. The Lyapunov exponents of the nine-term novel chaotic system are obtained as L1 1⁄4 9:45456; L2 1⁄4 0 and L3 1⁄4 30:50532. Since the maximal Lyapunov e...

In this paper, the authors propose a new chaotic block cryptosystem based on multiple one-dimensional chaotic maps. In the proposed cryptosystem, the authors establish map-to-task relations between the multiple chaotic maps and the tasks, which must be performed in the encryption rounds. The encryption process is based on these map-to-task relations. The authors enhance the security of the cryp...

Klaus Morawetz, Michael Vogt, Uwe Fuhrmann, Pavel Lipavský, Václav Špička 1 LPC, IN2P3-CNRS, ISMRA, 6 Bd du Marechal Juin, Caen, 14050, France 2 GANIL, B.P. 5027, Bd Henri Becquerel, 14076 Caen Cedex 5, France 3 Fachbereich Physik, University Rostock, D-18055 Rostock, Germany 4 Institute of Philosophy, University Rostock, D-18055 Rostock, Germany 5 Institute of Physics, Academy of Sciences, Cuk...

The aim of this paper is to prove the following results: a continuous map f : [0, 1]→ [0, 1] is chaotic iff the shift map σf : lim ← ([0, 1], f)→ lim ← ([0, 1], f) is chaotic. However, this result fails, in general, for arbitrary compact metric spaces. σf : lim ← ([0, 1], f) → lim ← ([0, 1], f) is chaotic iff there exists an increasing sequence of positive integers A such that the topological s...

in this paper we review some recent ideas of synchronization theory. we apply this theory to study the different synchronization aspects of uni-directionally coupled pair of chaotic one-dimensional gaussian maps.