Related papers: Global Attractor in Competitive Lotka-Volterra Sys…
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows…
We consider a generalized alpha-type model in the whole three-dimensional space and driven by a stationary (time-independent) external force. This model contains as particular cases some relevant equations of the fluid dynamics, among them…
We investigate linear-quadratic dynamical systems with energy preserving quadratic terms. These systems arise for instance as Galerkin systems of incompressible flows. A criterion is presented to ensure long-term boundedness of the system…
This paper studies the traveling wave solutions to a three species competition cooperation system. The existence of the traveling waves is investigated via monotone iteration method. The upper and lower solutions come from either the waves…
This paper considers the dynamical behavior of solutions of constitutive systems for 1D compressible viscous and heat-conducting micropolar fluids. With proper constraints on initial data, we prove the existence of global attractors in…
This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence…
For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…
We consider the Lotka-Volterra system and provide necessary conditions for an equilibrium to be stable. Our results naturally complement earlier fundamental results by N. Adachi, Y. Takeuchi, and H. Tokumaru, who, in a series of papers,…
We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law…
Based on previous work done in this field, we build a dynamical system that describes changes in drug addiction in an isolated population when two addictive substances are available simultaneously. We then use our model to investigate…
We consider an autonomous system of partial differential equations for one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases…
The eigenvalue spectrum of a random matrix often only depends on the first and second moments of its elements, but not on the specific distribution from which they are drawn. The validity of this universality principle is often assumed…
Using properties of asymptotically almost periodic solutions we prove existence theorem for piece-wise continuous almost periodic solutions of differential equations with delay and impulses. We apply these results to study almost periodic…
We present new a stability result for periodic solutions of the periodic predator prey Lotka Volterra model, based on boundaries for the average of the coexistence states. Our result complements previous one in the literature.
Seasonality frequently occurs in population models, and the corresponding seasonal patterns have been of great interest to scientists. This paper is concerned with traveling waves to a time-periodic bistable Lotka-Volterra competition…
In this paper we address a class of replicator dynamics, referred as polymatrix replicators, that contains well known classes of evolutionary game dynamics, such as the symmetric and asymmetric (or bimatrix) replicator equations, and some…
In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with…
Global dynamical behaviors of the competitive Lotka-Volterra system even in 3-dimension are not fully understood. The Lyapunov function can provide us such knowledge once it is constructed. In this paper, we construct explicitly the…
In this paper we study the structure of the global attractor for a reaction- di{\S}usion equation in which uniqueness of the Cauchy problem is not guarantied. We prove that the global attractor can be characterized using either the unstable…
Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two species Lotka-Volterra…