相关论文: Periodic orbits for periodic eco-epidemiological s…

We prove the existence of $n$-periodic orbits for almost all $n\in\mathbb{N}$ in the R\"ossler system with attracting periodic orbit, for two sets of parameters. The proofs are computer-assisted.

A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters…

We will show that if a dynamical system has enough constants of motion then a Moser-Weinstein type theorem can be applied for proving the existence of periodic orbits in the case when the linearized system is degenerate.

By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…

We investigate the natural families of periodic orbits associated with the equilibrium configurations of the the planar restricted $1+n$ body problem for the case $2\leq n \leq 4$ equal mass satellites. Such periodic orbits can be used to…

In this paper, we establish a new criterion for the orbital stability of periodic waves related to a general class of regularized dispersive equations. More specifically, we present sufficient conditions for the stability without knowing…

In this work, applying general results from averaging theory, we find periodic orbits for a class of Hamiltonian systems $H$ whose potential models the motion of elliptic galaxies.

By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…

We consider random perturbations of a general eco-epidemiological model. We prove the existence of a global random attractor, the persistence of susceptibles preys and provide conditions for the simultaneous extinction of infectives and…

We consider a predator-prey population model with prey gathering together for defense purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behavior, establishing that ultimately either only the…

Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the…

The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…

In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total…

We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…

We consider the billiard map inside a polyhedron. We give a condition for the stability of the periodic trajectories. We apply this result to the case of the tetrahedron. We deduce the existence of an open set of tetrahedra which have a…

In this paper we study the properties of the periodic orbits of \"x + V'_x(t, x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called {\rho} \in (1/T0)Q the frequency of windings of an orbit in S1 we show that exists an infinite…

We treat the periodic trajectory tracking problem: given a periodic trajectory of a control-affine, left-invariant driftless system in a compact and connected Lie group $G$ and an initial condition in $G$, find another trajectory of the…

In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…

We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…

We track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show…