Related papers: Dynamics of the optical swallowtail catastrophe
In several natural and engineering systems, changes in control parameters can trigger bifurcations that lead to sustained or growing periodic oscillations, indicating the onset of oscillatory instabilities. Such emergent behaviour often…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the…
The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed…
Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing…
Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…
Non-integrability in the sense of dynamical systems, also known as dynamical chaos, is a strongly nonlinear qualitative phenomenon. Its most promising theoretical descriptions are likely to emerge from non-perturbative approaches, with…
Unusual domains with curved walls and failure to satisfy the Landau-Lifshitz-Kittel Law are modeled as folding catastrophes (saddle-node bifurcations). This description of ballistic motion in a viscous medium is based upon early work by…
Deterministic chaos is commonly associated with spectral criticality: exponential sensitivity is expected when Jacobian eigenvalues exceed unity in parts of the attractor, producing the local expansion that offsets contraction elsewhere. We…
We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the…
Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counterrotating Taylor-Couette system that were done for fixed axial wavelengths are…
We show how coupling an ensemble of bistable systems to a common cavity field affects the collective stochastic behavior of this ensemble. In particular, the cavity provides an effective interaction between the systems, and parametrically…
We present a comprehensive discussion of a transition from integrability to non-integrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter $\epsilon$, which modifies the boundary shape…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability…
In transport processes across materials like glasses, living cells, and porous media, the probability density function of displacements exhibits exponential decay rather than Gaussian behavior. We show that this universal behavior of rare…
A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a…
This paper is concerned with the analysis of a class of impacting systems of relevance in applications: cam-follower systems. We show that these systems, which can be modelled as discontinuously forced impact oscillators, can exhibit…
This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…