Related papers: Instability and Chaos in Non-Linear Wave Interacti…
We study nonlinear dynamics in a system of two coupled oscillators, describing the motion of two interacting microbubble contrast agents. In the case of identical bubbles, the corresponding symmetry of the governing system of equations…
An analysis of transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces is presented. The synchronization phenomenon is investigated in the ensemble of particles moving…
This paper presents a new systematic framework for nonlinear singularly perturbed systems in which state-dependent perturbation functions are used instead of constant perturbation coefficients. Under this framework, general results are…
In this paper, the interaction of an incident finite amplitude longitudinal wave with a localized region of nonlinearity is considered. This interaction produces a secondary field represented by a superposition of first-, second-, and…
We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare current versus fluctuations driven networks, the former (latter) is…
The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…
The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are…
In two previous papers the author described ``Islands of Instability" that may appear in wavefunction models with nonlinear evolution (of a type proposed originally in the context of the Measurement Problem). Such ``IsoI" represent a new…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
Analytical and numerical modelling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium…
We describe the emergence and interactions of breather modes and resonant wave modes within a two-dimensional ring-like oscillator chain in a microcanonical situation. Our analytical results identify different dynamical regimes…
We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are super-exponentially localized, and present an accurate numerical method allowing to find…
We investigate analytically and numerically the conditions for the Turing instability to occur in a one-dimensional chain of nonlinear oscillators coupled non-locally in such a way that the coupling strength decreases with the spatial…
The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While…
We consider a quantum space with rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains tensors of noncommutativity constructed involving additional coordinates and momenta. In the rotationally…