We propose a robust method that allows a periodic or a chaotic multi-stable system to be transformed to a monostable system at an orbit with dominant frequency of any of the coexisting attractors. Our approach implies the selection of a particular attractor by periodic external modulation with frequency close to the dominant frequency in the power spectrum of a desired orbit and simultaneous an...

In a gravitational force field, a bounded orbit of an infinitesimal point mass is called a satellite orbit. The purpose of this paper is to establish a variational theory for the existence of some relative periodic satellite orbits in periodic gravitational force fields. The gravitation field can be generated by a relative equilibrium or a uniformly rotating asteroid. Our approach is to regard ...

In many problems of quantum chaos the calculation of sums of products of periodic orbit contributions is required. A general method of computation of these sums is proposed for generic integrable models where the summation over periodic orbits is reduced to the summa-tion over integer vectors uniquely associated with periodic orbits. It is demonstrated that in multiple sums over such integer ve...

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...

Elaydi and Yakubu showed that a globally asymptotically stable(GAS) periodic orbit in an autonomous difference equation must in fact be a fixed point whenever the phase space is connected. In this paper we extend this result to periodic nonautonomous difference equations via the concept of skew-product dynamical systems. We show that for a k-periodic difference equation, if a periodic orbit of ...

A solution of the Abel equation ẋ = A(t)x + B(t)x such that x(0) = x(1) is called a periodic orbit of the equation. Our main result proves that if there exist two real numbers a and b such that the function aA(t) + bB(t) is not identically zero, and does not change sign in [0, 1] then the Abel differential equation has at most one nonzero periodic orbit. Furthermore, when this periodic orbit ex...

Let T be a tree with n vertices. Let f : T → T be continuous and suppose that the n vertices form a periodic orbit under f . We show: (1) (a) If n is not a divisor of 2k then f has a periodic point with period 2k. (b) If n = 2pq, where q > 1 is odd and p ≥ 0, then f has a periodic point with period 2pr for any r ≥ q. (c) The map f also has periodic orbits of any period m where m can be obtained...

We consider the problem of stochastic exit from a planar domain, whose boundary is an unstable periodic orbit, and which contains a stable periodic orbit. This problem arises when investigating the distribution of noise-induced phase slips between synchronized oscillators, or when studying stochastic resonance far from the adiabatic limit. We introduce a simple, piecewise linear model equation,...