相关论文: Approximation of the generalized principal eigenva…

It is well known that, in the study of the dynamical properties of nonlinear reaction-diffusion systems, the sign of the principal eigenvalue of the linearized system plays an important role. However, for the nonlocal dispersal systems, due…

The current paper {establishes} criteria for the existence of principal eigenvalues of time periodic cooperative linear nonlocal dispersal systems with Direchlet type, Neumann type or periodic type boundary conditions. It is shown that such…

The principal eigenvalue for linear elliptic operator has been known to be one of very useful tools to investigate many important partial differential equations. Due to the pioneering works of Berestycki et al. \cite{BCV1,BCV2}, the study…

This paper is mainly concerned with the generalised principal eigenvalue for time-periodic nonlocal dispersal operators. We first establish the equivalence between two different characterisations of the generalised principal eigenvalue. We…

This paper develops the notion and properties of the generalized principal eigenvalue for an elliptic system coupling an equation in a plane with one on a line in this plane, together with boundary conditions that express exchanges taking…

This paper is concerned with generalizations of the notion of principal eigenvalue in the context of space-time periodic cooperative systems. When the spatial domain is the whole space, the Krein-Rutman theorem cannot be applied and this…

The basic reproduction ratio is a crucial threshold parameter in infectious disease models. In nonlocal dispersal systems, its variational characterization is challenging due to the possible absence of a principal eigenvalue caused by…

We consider general linear non-degenerate weakly-coupled cooperative elliptic systems and study certain monotonicity properties of the generalized principal eigenvalue in $\mathbb{R}^d$ with respect to the potential. It is shown that…

In this communication, we prove some important limits of the principal eigenvalue for nonlocal operator of Neumann type with respect to the parameters, which are significant in the understanding of dynamics of biological populations. We…

In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…

In this paper, we propose and analyze a nonlocal cooperative reaction--diffusion system with free boundaries and drift terms, motivated by directional epidemic spread. Lacking a variational structure but requiring sharper regularity of…

We address the count of isolated and embedded eigenvalues in a generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue…

We address the variational problem for the generalized principal eigenvalue on $\mathbb{R}^d$ of linear and semilinear elliptic operators associated with nondegenerate diffusions controlled through the drift. We establish the…

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…

The purpose of this paper is to investigate the principal spectral theory and asymptotic behavior of the spectral bound for cooperative nonlocal dispersal systems, specifically focusing on the case where partial diffusion coefficients are…

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…

This paper is devoted to the study of the asymptotic behavior of the principal eigenvalue and basic reproduction ratio associated with periodic population models in a patchy environment for small and large dispersal rates. We first deal…

In this paper we investigate the dynamical properties of a spatially periodic reaction-diffusion system {whose reaction terms are of hybrid nature in the sense that they are partly competitive and partly cooperative depending on the value…

For continuous-time dynamical systems with reversible trajectories, the nowhere-vanishing eigenfunctions of the Koopman operator of the system form a multiplicative group. Here, we exploit this property to accelerate the systematic…

This paper classifies the set of supersolutions of a general class of periodic-parabolic problems in the presence of a positive supersolution. From this result we characterize the positivity of the underlying resolvent operator through the…