相关论文: Benjamin-Feir instabilities on directed networks
We examine the instabilities of a confined active nematic subjected to an orienting field using a low Reynolds number Ericksen-Leslie framework with active stresses and field-induced torques. Linear analysis reveals two distinct modes, with…
We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and…
In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks.…
We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we…
We present the theory of modulation instability induced by spectrally dependent losses (optical filters) in passive driven nonlinear fiber ring resonators. Starting from an Ikeda map description of the propagation equation and boundary…
In this work, the Ginzburg-Landau theory is represented on a symplectic manifold with a phase space content. The order parameter is defined by a quasi-probability amplitude, which gives rise to a quasi-probability distribution function,…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
We study the dynamics of nonlinear random walks on complex networks. We investigate the role and effect of directed network topologies on long-term dynamics. While a period-doubling bifurcation to alternating patterns occurs at a critical…
Theoretical and experimental study of high-acceleration patterns in vibrated granular layers is presented. The order parameter model based on parametric Ginzburg-Landau equation is used to describe strongly nonlinear excitations including…
Transverse instability of a bunched beam is investigated with synchrotron oscillations, space charge, and resistive wall wakefield taken into account. Boxcar model is used for all-round analysis, and Gaussian distribution is invoked for…
This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar…
The problem of the existence of an analytic normal form near an equilibrium point of an area-preserving map and analyticity of the associated coordinate change is a classical problem in dynamical systems going back to Poincar\'e and Siegel.…
The study of dynamical systems on complex networks is of paramount importance in engineering, given that many natural and artificial systems find a natural embedding on discrete topologies. For instance, power grids, chemical reactors and…
The influence of small additive noise on structure formation near a forwards and near an inverted bifurcation as described by a cubic and quintic Ginzburg Landau amplitude equation, respectively, is studied numerically for group velocities…
A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general equation for the densities of force chains in different directions is proposed and a complete solution is…
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…
We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling…
There are a number of models of coupled oscillator networks where the question of the stability of fixed points reduces to calculating the index of a graph Laplacian. Some examples of such models include the Kuramoto and Kuramoto--Sakaguchi…
In hierarchical triple systems, the inner binary is slowly perturbed by a distant companion, giving rise to large-scale oscillations in eccentricity and inclination, known as von-Zeipel-Lidov-Kozai (ZLK) oscillations. Stable systems with a…