Related papers: Replicate Periodic Windows in the Parameter Space …
We demonstrate with a minimal example that in Filippov systems (dynamical systems governed by discontinuous but piecewise smooth vector fields) stable periodic motion with sliding is not robust with respect to stable singular perturbations.…
In diverse physical systems stable oscillatory solutions devolve into more complicated dynamical behaviour through border-collision bifurcations. Mathematically these occur when a stable fixed point of a piecewise-smooth map collides with a…
The paper revisits a well-known model of forced vibro-impact oscillator with Amonton-Coulomb friction. In vast majority of the existing studies, this model included also viscous friction, and its global dynamics in the state space is…
We discuss the influence of periodic orbits on the dissociation of a model diatomic molecule driven by a strong bichromatic laser fields. Through the stability of periodic orbits we analyze the dissociation probability when parameters like…
In this paper we start a global study of the parameter space (dissipation, perturbation, frequency) of the dissipative spin-orbit problem in Celestial Mechanics with the aim of delimiting regions where the dynamics, or at least some of its…
The scope of the paper is the analysis of the impact of flow reversal on the dynamics of cascades of reactors. Periodic and chaotic oscillations occur in the analyzed system. There is a dependence between the oscillation period of the state…
Impacting mechanical systems with suitable parameter settings exhibit a large amplitude chaotic oscillation close to the grazing with the impacting surface. The cause behind this uncertainty is the square root singularity and the occurrence…
This paper introduces the notion of second minimal $n$-periodic orbit of the continuous map on the interval according as if $n$ is a successor of the minimal period of the map in Sharkovski ordering. We pursue classification of second…
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress…
Arrays of coupled semiconductor lasers are systems possessing radically complex dynamics that makes them useful for numerous applications in beam forming and beam shaping. In this work, we investigate the spatial controllability of…
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest neighbor interactions,…
Parametrically driven oscillators can display period-tripling in response to a drive at thrice the resonance frequency. In contrast to the parametric instability for period doubling, the symmetric fixed-point corresponding to the state of…
We study order-parameter fluctuations (OPF) in disordered systems by considering the behavior of some recently introduced paramaters $G,G_c$ which have proven very useful to locate phase transitions. We prove that both parameters G (for…
As the parameters of a map are varied an attractor may vary continuously in the Hausdorff metric. The purpose of this paper is to explore the continuation of chaotic attractors. We argue that this is not a helpful concept for smooth…
We study the dynamics of a mechanical oscillator with linear and cubic forces -the Duffing oscillator- subject to a feedback mechanism that allows the system to sustain autonomous periodic motion with well-defined amplitude and frequency.…
Oscillatory reconnection is a time-dependent magnetic reconnection mechanism that naturally produces periodic outputs from aperiodic drivers. This paper aims to quantify and measure the periodic nature of oscillatory reconnection for the…
We perform spectral simulations of dynamo for magnetic Prandtl number of one with Taylor-Green forcing. We observe dynamo transition through a supercritical pitchfork bifurcation. Beyond the transition, the numerical simulations reveal…
The propulsion type plasma in oblique external magnetic field is studied in 2D3V PIC MCC simulations. A periodical structure with maxima of electron and ion densities appears with an increase of an obliqueness of magnetic field. These…
Spatio-temporal chaos in parametrically driven waves is investigated in one and two dimensions using numerical simulations of Ginzburg-Landau equations. A regime is identified in which in one dimension the dynamics are due to double phase…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…