Related papers: Spatio-temporal dynamics for a class of monotone e…

In this paper,under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone evolution systems without spatial translation invariance.…

This paper is devoted to the study of propagation dynamics for a large class of non-monotone evolution systems. In two directions of the spatial variable, such a system has two limiting systems admitting the spatial translation invariance.…

Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…

This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…

The limiting stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literature. In this paper we initially initiate a program to study…

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…

We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…

We consider a continuum aggregation model with nonlinear local repulsion given by a degenerate power-law diffusion with general exponent. The steady states and their properties in one dimension are studied both analytically and numerically,…

A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…

We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…

We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…

A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…

In this paper, we investigate a class of non-monotone reaction-diffusion equations with distributed delay and a homogenous boundary Neumann condition, which have a positive steady state. The main concern is the global attractivity of the…

In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…

In this paper, we study a diffusive Lotka-Volterra competition model under homogeneous Dirichlet boundary conditions. We shall discuss the effects of dispersal rate and spatial heterogeneity on population dynamics. More precisely, we…

We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…

In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator-prey systems with density-dependent preytaxis in a two-dimensional bounded domain with Neumann boundary conditions, where the…

We show that a sub-homogeneous positive monotone system with bounded heterogeneous time-varying delays is globally asymptotically stable if and only if the corresponding delay-free system is globally asymptotically stable. The proof is…

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…

In this work, we characterize a class of nonlinear monotone dynamical systems that have a certain translation invariance property which goes by the name of plus-homogeneity; usually called "topical" systems. Such systems need not be…