This paper is concerned with chaos of a family of logistic maps. It is first proved that a regular and nondegenerate snap-back repeller implies chaos in the sense of both Devaney and Li-Yorke for a map in a metric space. Based on this result, it is shown that the logistic system is chaotic in the sense of both Devaney and Li-Yorke, and has uniformly positive Lyapunov exponents in an invariant s...

In this letter, chaos in a current-mode controlled boost converter is studied. Firstly, the existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of a one-sided shift map, which implies positive entropy of the system and hence chaotic behavior. The essential tool is the horseshoe hypotheses proposed by K...

This paper is concerned with chaos induced by regular snap-back repellers. One new criterion of chaos induced by strictly coupled-expanding maps in compact sets of metric spaces is established. By employing this criterion, the nondegenerateness assumption in the Marotto theorem established in 1978 is weakened. In addition, it is proved that a regular snap-back repeller and a regular homoclinic ...

A new mathematical concept of abstract similarity is introduced and illustrated in the space infinite strings on a finite number symbols. The problem chaos presence for Sierpinski fractals, Koch curve, as well Cantor set solved by considering natural map. This accomplished Poincaré, Li-Yorke Devaney chaos, including multi-dimensional cases. Original numerical simula...