A coupled system of two generalized logistic maps is studied. In particular influence of the coupling to the behaviour of the Julia set in two dimensional complex space is analyzed both analytically and numerically. It is proved analytically that the Julia set disappears from the complex plane uniformly as a parameter interpolates from the chaotic phase to the integrable phase, if the coupling ...

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. Unfortunately, despite the advantages of chaotic systems, Such as, noise-like correlation, easy hardware implementation, multitude of chaotic modes, flexible control of their dynamics, chaotic self-synchronization phenomena and potential communication confidence due to the very dynami...

Ant algorithms are usually derived from a stochastic modeling based on some specific probability laws. We consider in this paper a full deterministic model of “logistic ants” which uses chaotic maps to govern the behavior of the artificial ants. We illustrate and test this approach on a TSP instance, and compare the results with the original Ant System algorithm. This change of paradigm —determ...

– We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the ordered phase of these systems. The transient times necessary to reach the asymptotic states can be very long, especially very near the transition line separatin...

Chaos theory has significantly contributed towards the development of fast and secure image encryption algorithms. Authors in [1] proposed an efficient and secure approach for image encryption based on chaotic logistic maps. The algorithm uses an 80-bit secret key and two chaotic logistic maps, whose initial conditions are derived using the secret key. Depending upon the outcome of logistic map...