Related papers: Symmetry breaking perturbations and strange attrac…

The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains the non-interacting sector and the diagonal elements of Fock space from the interacting terms. The…

We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a…

This paper studies hidden oscillations appearing in electromechanical systems with and without equilibria. Three different systems with such effects are considered: translational oscillator-rotational actuator, drilling system actuated by a…

Geometrical properties of two-dimensional mixtures near the jamming transition point are numerically investigated using harmonic particles under mechanical training. The configurations generated by the quasi-static compression and…

We study nonlinear dynamics in a model of three interacting encapsulated gas bubbles in a liquid. The model is a system of three coupled nonlinear oscillators with an external periodic force. Such bubbles have numerous applications, for…

We investigate the impact of nonlinear damping on the dynamics of a nanomechanical doubly clamped beam. The beam is driven into nonlinear regime and the response is measured by a displacement detector. For data analysis we introduce a…

This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…

In this paper we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both…

Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…

We consider heteroclinic attractor networks motivated by models of competition between neural populations during binocular rivalry. We show that Gamma distributions of dominance times observed experimentally in binocular rivalry and other…

Symmetry breaking of continuous symmetries by extended dynamical defects entails the existence of defect families, which form conformal manifolds in a critical setup. In the presence of bulk 't Hooft anomalies, defects are in fact required…

A chaotic autonomous Hamiltonian systems, perturbed by small damping and small external force, harmonically dependent on time, can acquire a strange attractor with properties similar to that of the canonical distribution - the Gibbs…

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…

By means of an updated renormalization method, we construct asymptotic expansions for unstable manifolds of hyperbolic fixed points in the double-well map and the dissipative H\'enon map, both of which exhibit the strong homoclinic chaos.…

We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of…

We study the dissipative quantum Duffing oscillator in the deep quantum regime with two different approaches: The first is based on the exact Floquet states of the linear oscillator and the nonlinearity is treated perturbatively. It well…

We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise…

The effect of small nonlinear dissipation on the dynamics of system with stochastic web which is linear oscillator driven by pulses is studied. The scenario of coexisting attractors evolution with the increase of nonlinear dissipation is…

The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in…

In this paper, we study the dynamics and stability of a fundamental power system model when a time delay is imposed on the excitation of the generator. It is observed that sustained oscillations can arise in an otherwise stable power system…