Related papers: Dynamics of symmetric dynamical systems with delay…
Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…
Instead of the conventional construction of symmetric and antisymmetric states by abruptly projecting with the symmetrizer or antisymmetrizer, this paper investigates rapid but continuous symmetrization via environment-induced decoherence.…
Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics are determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a…
This paper investigates the global structures of periodic orbits that appear in Rayleigh-B\'enard convection, which is modeled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the…
For the discrete-time dynamical system generated by the Poincare map T of a time-periodic closed-loop negative feedback system, we present an amenable condition which enables us to obtain the global convergence of the orbits. This yields…
We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincar\'e maps to study the dynamics of some bounded, eternal…
A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables…
A recent work by the authors on the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in delay differential equations motivates the derivation of periodic normal forms. In this paper, we prove the…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
We analyze planar $n$-body Hamiltonian systems with quadratic $D_n$-invariant interactions and identify the symmetry obstruction to choreographic motion. Choreographies are taken throughout to be collision-free solutions of the equations of…
We consider the scalar delay differential equation $$ \dot{x}(t)=-x(t)+f_{K}(x(t-1)) $$ with a nondecreasing feedback function $f_{K}$ depending on a parameter $K$, and we verify that a saddle-node bifurcation of periodic orbits takes place…
We obtain a description of the Poincar\'e recurrences of chaotic systems in terms of the ergodic theory of transient chaos. It is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by…
Optical systems that combine nonlinearity with coupling between various subsystems offer a flexible platform for observing a diverse range of nonlinear dynamics. Furthermore, engineering tolerances are such that the subsystems can be…
Periodic orbits of systems of ordinary differential equations can be found and continued numerically by following fixed points of Poincar\'e maps. However, this often fails near grazing bifurcations where a periodic orbit collides…
The dynamics of one-way coupled systems with discrete time is considered. The behavior of the coupled logistic maps is compared to the dynamics of maps obtained using the Poincare sectioning procedure applied to the coupled continuous-time…
A perturbed family of interval exchange maps (FIEMs) provides a natural two-\linebreak{}dimensional area-preserving extension of interval exchange maps, with each IEM parameterized by an action variable $y$. Such families arise, for…
For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…
We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge'' orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios…
In the present paper, we study the Poincare map associated to a periodic perturbation, both in space and time, of a linear Hamiltonian system. The dynamical system embodies the essential physics of stellar pulsations and provides a global…
We study the quasi-periodicity phenomena occurring at the transition between tonic spiking and bursting activities in exemplary biologically plausible Hodgkin-Huxley type models of individual cells and reduced phenomenological models with…