Related papers: Stability of Boolean and continuous dynamics
We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic,…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
Quantum droplets are ultradilute liquid states which emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of…
The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally…
Coregulation of the expression of groups of genes has been extensively demonstrated empirically in bacterial and eukaryotic systems. Such coregulation can arise through the use of shared regulatory motifs, which allow the coordinated…
The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary…
Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in…
In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…
The stability of quantum systems to perturbations of the Hamiltonian is studied. This stability is quantified by the fidelity. Dependence of fidelity on the initial state as well as on the dynamical properties of the system is considered.…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
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,…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…