In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itse...

In a recent paper [Melby P, Kaidel J, Weber N, Hubler A. Adaptation to the edge of chaos in the self-adjusting logistic map. Phys Rev Lett 2000;84:5991–3], Melby et al. attempted to understand edge of chaos behaviour through a very simple model. Based on our exhaustive numerical experiments, here we show that the model, with the definition of the edge of chaos given in the paper, cannot unequiv...

Several chaotic properties of cyclic permutation maps are considered. Cyclic refer to p-dimensional dynamical systems the form φ(b1,b2,⋯,bp)=(up(bp),u1(b1),⋯,up−1(bp−1)), where bj∈Hj (j∈{1,2,⋯,p}), p≥2 is an integer, and Hj (j∈{1,2,⋯,p}) compact subintervals real line R=(−∞,+∞). uj:Hj→Hj+1(j=1,2,…,p−1) up:Hp→H1 continuous maps. Necessary sufficient conditions for a class have Li–Yorke chaos, di...

Analyses and investigations on river flow behavior are major issues in design, operation and studies related to water engineering. Thus, recently the application of chaos theory and new techniques, such as chaos theory, has been considered in hydrology and water resources due to relevant innovations and ability. This paper compares the performance of chaos theory with Anfis model and discusses ...

in this research prediction methods of artificial neural network and chaos theory are employed to predict daily, weekly and monthly runoff. for this, runoff series data observed at pole-kohneh located in the qareh-soo river. the nonlinear predictions of chaos are found to be in close agreement with the observed runoff, with high correlation coefficient for daily and weekly time scales. predicte...