Related papers: Periodic orbits for periodic eco-epidemiological s…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We give a necessary and sufficient condition for strong stability of low dimensional Hamiltonian systems, in terms of the iterates of a closed orbit and the Conley-Zehnder index. Applications to Mathieu equation and stable harmonic…
The orbits about Lagrangian equilibrium points are important for scientific investigations. Since, a number of space missions have been completed and some are being proposed by various space agencies. In light of this, we consider a more…
In this paper we consider a one dimensional liner piecewise-smooth discontinuous map. It is well known that stable periodic orbits exist in this type of map for a specific parameter region. It is also known that the corresponding…
We prove the existence of periodic orbits of the two fixed centers problem bifurcating from the Kepler problem. We provide the analytical expressions of these periodic orbits when the mass parameter of the system is sufficiently small.
Piecewise smooth maps are known to exhibit a wide range of dynamical features including numerous types of periodic orbits. Predicting regions in parameter space where such periodic orbits might occur and determining their stability is…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
We derive characteristic functions to determine the number and stability of relaxation oscillations for a class of planar systems. Applying our criterion, we give conditions under which the chemostat predator-prey system has a globally…
This paper considers the optimal control problem of connecting two periodic trajectories with maximal persistence. A maximally persistent trajectory is close to the periodic type in the sense that the norm of the image of this trajectory…
We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the…
For many measure preserving dynamical systems $(\Omega,T,m)$ the successive hitting times to a small set is well approximated by a Poisson process on the real line. In this work we define a new process obtained from recording not only the…
We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a general…
Planetary debris is observed in the atmospheres of over 1,000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense.…
By applying a Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence of a periodic solution for a class of impulsive neutral differential equations. The procedure adopted in this…
It is often assumed that a warped galaxy can be modeled by a set of rings. This paper verifies numerically the validity of this assumption by the study of periodic orbits populating a heavy self-gravitating warped disk. The phase space…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…
As a contribution to the inverse scattering problem for classical chaotic systems, we show that one can select sequences of intervals of continuity, each of which yields the information about period, eigenvalue and symmetry of one unstable…
In this paper we consider periodic orbits of planar linear Filippov systems with a line of discontinuity. Unlike many publications researching only the maximum number of crossing periodic orbits, we investigate not only the number and…