Related papers: Coarsening to Chaos-Stabilized Fronts
We present a simple model of alignment of a large number of rigid bodies (modeled by rotation matrices) subject to internal rotational noise. The numerical simulations exhibit a phenomenon of first order phase transition with respect the…
We propose a generalized parity-time ($\mathcal{PT}$) -symmetric Li\'enard oscillator with two different orders of nonlinear position-dependent dissipation. We study the stability of the stationary states by using the eigenvalues of…
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
The growth of laminar-turbulent band patterns in plane Couette flow is studied in the vicinity of the global stability threshold R_g below which laminar flow ultimately prevails. Appropriately tailored direct numerical simulations are…
In this paper, we study dynamical systems in which a large number $N$ of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and…
We consider a chain of nonlinear oscillators with long-range interaction of the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha <2. In the continues limit the system's dynamics is described by the Ginzburg-Landau…
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for parametrically driven waves. The motion of the defects is traced in detail yielding their life-times, annihilation partners, and distances traveled. In a regime in…
This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
The steady-state of a generalized coagulation-decoagulation model on a one-dimensional lattice with reflecting boundaries is studied using a matrix-product approach. It is shown that the quadratic algebra of the model has a four-dimensional…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…
It has long been known that complex balanced mass-action systems exhibit a restrictive form of behaviour known as locally stable dynamics. This means that within each compatibility class $\mathcal{C}_{\mathbf{x}_0}$---the forward invariant…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…