Related papers: Master stability for traveling waves on networks
In this paper, we present a complete classification of traveling wave solutions for monostable systems within a unified framework. To this end, we introduce a novel technique, referred to as the slicing method, which is based on the…
We consider a network of identical piecewise smooth systems that synchronizes on the manifold given by a periodic orbit of a single agent. We explicitly characterize the fundamental matrix solution of the network along the synchronous…
We study a Rock-Paper-Scissors model for competing populations that exhibits travelling waves in one spatial dimension and spiral waves in two spatial dimensions. A characteristic feature of the model is the presence of a robust…
We consider a ring of identical or near identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the…
We prove a principle of linearized stability for traveling wave solutions to neural field equations posed on the real line. Additionally, we provide the existence of a finite dimensional invariant center manifold close to a traveling wave,…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on…
Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for…
The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchronization in large oscillator networks.…
Superconductor stability is at the core of the design of any successful cable and magnet application. This chapter reviews the initial understanding of the stability mechanism, and reviews matters of importance for stability such as the…
Synchronization phenomena are of broad interest across disciplines and increasingly of interest in a multiplex network setting. Here we show how the Master Stability Function, a celebrated framework for analyzing synchronization on a single…
This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…
In this paper, we investigate the instability of the spherical travelling wave solutions for the Transport-Stokes system in $\mathbb{R}^3$. First, a classical scaling argument ensures instability among all probability measures for the…
In this paper, we investigate the modulational stability of periodic traveling waves in a local model for shallow water waves, which is an extended version of the Hunter-Saxton equation. We construct a family of small-amplitude periodic…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…
In this paper we establish a necessary and sufficient stability condition for a stochastic ring network. Such networks naturally appear in a variety of applications within communication, computer, and road traffic systems. They typically…
In this paper, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method we find explict periodic waves and we also present a characterization for all…
Discrete nonlinear systems support a rich variety of localized and extended wave phenomena, with their dynamics sensitively dependent on the symmetries of the underlying interaction forces within the lattice. Odd elasticity, emerging in…
We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability…
For coupled oscillator networks with Laplacian coupling the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous state. Using tools from group theory this approach has…