We show sensitive dependence on initial conditions and dense set of periodic points imply asymptotic sensitivity, a stronger form of sensitivity , where the deviation happens not just once but infinitely many times. As a consequence it follows that all Devaney chaotic systems (e.g. logistic map) have this asymptotic sensitivity. Sensitive dependence on initial conditions (shortly, sensitivity) ...

We study the set of strictly temporally periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but are not spatially periodic. This set turns out to be residual for equicontinuous surjective cellular automata, dense for almost equicontinuous surjective cellular automata, while it is empty for the positively expa...

Dynamical systems generated by d > 2 commuting homeomorphisms (topological Zd-actions) contain within them structures on many scales, and in particular contain many actions of Zk for 1 6 k 6 d. Familiar dynamical invariants for homeomorphisms, like entropy and periodic point data, become more complex and permit multiple definitions. We briefly survey some of these and other related invariants i...

For the class of permutive cellular automata the number of periodic points and the topological and metrical entropies are calculated.

It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. We had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove that S is a nowhere dense subset of [0,1] if and only if {f...

The problem of pole assignment, also known as an eigenvalue assignment, in linear discrete-time periodic systems in discs was solved by a novel method which employs elementary similarity operations. The former methods tried to assign the points inside the unit circle while preserving the stability of the discrete time periodic system. Nevertheless, now we can obtain the location of eigenvalues ...

Let f be a continuous map of the circle into itself . The main purpose of this paper is to study the properties of the unstable manifold associated to a periodic point of f . Let 2(f) denote the nonwandering set of f . Suppose f has finitely many periodic points . Then, using the unstable manifolds associated to periodic points of f, three theorems are proved providing complete answers to the f...

The study of differential equations is useful in to analyze the possible past or future with help of present information. In this paper, the behavior of solutions has been analyzed around the equilibrium points for Gause model. Finally, some results are worked out to exist the stable periodic orbit for mentioned predator-prey system.