Related papers: Dynamics of phase slips in systems with time-perio…
The nonlinear dynamics of circularly polarized dispersive Alfv{\'e}n wave (AW) envelopes coupled to the driven ion sound waves of plasma slow response is studied in a uniform magnetoplasma. By restricting the wave dynamics to a few number…
We subject the steady solutions of a spherically symmetric accretion flow to a time-dependent radial perturbation. The equation of the perturbation includes nonlinearity up to any arbitrary order, and bears a form that is very similar to…
The selective frequency damping method was applied to a bent flow. The method was used in an adaptive formulation. The most dangerous frequency was determined by solving an eigenvalue problem. It was found that one of the patterns,…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…
Extending investigations of Antman & Malek-Madani, Schecter & Shearer, Slemrod, Barker & Lewicka & Zumbrun, and others, we investigate phase-transitional elasticity models of strain-gradient effect. We prove the existence of non-constant…
The susceptibility of timestepping algorithms to numerical instabilities is an important consideration when simulating partial differential equations (PDEs). Here we identify and analyze a pernicious numerical instability arising in…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
Turbulent systems exhibit a remarkable multi-scale complexity, in which spatial structures induce scale-dependent statistics with strong departures from Gaussianity. In Fourier space, this is reflected by pronounced phase synchronization. A…
Traveling waves triggered by a phase slip in coupled map lattices are studied. A local phase slip affects globally the system, which is in strong contrast with kink propagation. Attractors with different velocities coexist, and form…
Previously, a series of tidally-excited oscillations were discovered in the eccentric eclipsing binary KIC 3230227. The pulsation amplitudes and phases suggest the observed oscillations are prograde quadruple modes. In this paper, we refine…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the…
The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible…
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time…
In this Letter we show how the nonlinear evolution of a resonant triad depends on the special combination of the modes' phases chosen according to the resonance conditions. This phase combination is called dynamical phase. Its evolution is…
We consider the problem of stochastic exit from a planar domain, whose boundary is an unstable periodic orbit, and which contains a stable periodic orbit. This problem arises when investigating the distribution of noise-induced phase slips…
The coupled cluster iteration scheme is analysed as a multivariate discrete-time map using nonlinear dynamics and synergetics. The nonlinearly coupled set of equations to determine the cluster amplitudes are driven by a fraction of the…
The resonant quantum dynamics of an excited two-level emitter is investigated via classical modulation of its transition frequency while simultaneously the radiator interacts with a broadband electromagnetic field reservoir. The frequency…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some…