Related papers: Generalized Lotka-Volterra Systems and Complex Bal…
We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities…
Species-rich ecosystems often exhibit multiple stable states with distinct species compositions. Yet, the factors determining the likelihood of each state's occurrence remain poorly understood. Here, we characterize and explain the…
We study a novel general class of multidimensional type-I backward stochastic Volterra integral equations. Toward this goal, we introduce an infinite dimensional system of standard backward SDEs and establish its well-posedness, and we show…
We study the stability properties and long-term dynamical behavior of chimera states in globally coupled map lattices. In particular, we give a formula for the transverse Lyapunov exponent associated with blocks of synchronized sites. We…
We study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in two previous articles to prove the convergence to a unique stable equilibrium.
We present a possible approach to measuring inequality in a system of coupled Fokker-Planck-type equations that describe the evolution of distribution densities for two populations interacting pairwise due to social and/or economic factors.…
We present novel sufficient conditions for the global stability of equilibria in the case of nonlinear dynamics with analytic vector fields. These conditions provide stability criteria that are directly expressed in terms of the Taylor…
A general class of cross-diffusion systems for two population species in a bounded domain with no-flux boundary conditions and Lotka-Volterra-type source terms is analyzed. Although the diffusion coefficients are assumed to depend linearly…
In this paper, we introduce and analyze an asymptotic-preserving scheme for Lotka-Volterra parabolic equations. It is a class of nonlinear and nonlocal stiff equations, which describes the evolution of a population structured with…
We describe a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bounded sets; it contains all forward-time limit points. Our…
In this paper, we are concerned with the permanence of a Lotka-Volterra model of three competing species with seasonal succession. Based on the existence of a carrying simplex, that is a globally attracting hypersurface of codimension one,…
Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in \emph{Phys.…
In this paper we consider the existence of standing waves for a coupled system of $k$ equations with Lotka-Volterra type interaction. We prove the existence of a standing wave solution with all nontrivial components satisfying a prescribed…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
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…
Robert May famously used random matrix theory to predict that large, complex systems cannot admit stable fixed points. However, this general conclusion is not always supported by empirical observation: from cells to biomes, biological…
In this second part of the series, we investigate the uniqueness of positive fixed points of the Poincare map associated with the 3-dimensional Lotka-Volterra competition model with seasonal succession. Building on our first part of the…
The forces which drive growth, development, survival and change within an ecological system involving a predator and prey specie are not easily addressed in the field. To better understand the dynamics in the system, ecologists have turned…
This paper is concerned with a diffusive Lotka-Volterra cooperative modelwith population flux by attractive transition. We study the time-global well-posedness and the large time behavior of solutions in a case where the habitat is a…
A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior…