In this paper, we study the traveling front solutions of the LotkaVolterra competition-diffusion system with bistable nonlinearity. It is wellknown that the wave speed of traveling front is unique. Although little is known for the sign of the wave speed. In this paper, we first study the standing wave which gives some criteria when the speed is zero. Then, by the monotone dependence on paramete...

In this paper we study a discrete Raman laser amplification model given as a LotkaVolterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We construct numerical schemes for the approximation of the solution that have goo...

A non-autonomous nonlinear system with a time-variational forcing term is considered. For such a system, the global attraction of the origin is discussed, whose result is suggestive to an ecological problem as well because the system is reduced to a LotkaVolterra predator-prey model with prey receiving an environmental time-variation by an appropriate transformation. A numerical simulation is a...

The existence of positive periodic solutions of a periodic LotkaVolterra type competition system with delays and feedback controls is studied by applying the continuation theorem of coincidence degree theory. By contracting a suitable Liapunov functional, a set of sufficient conditions for the global asymptotic stability of the positive periodic solution of the system is given. A counterexample...

In this paper we study a discrete Raman laser amplification model given as a LotkaVolterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good s...

The coexistence and global stability of population models are of the interesting subjects in mathematical biology. Many authors have argued that the discrete time models are governed by differential equations which are more appropriate than the continuous ones to describe the dynamics of population when the population has nonoverlapping generations, a lot has been done on discrete Lotka-Volterr...

In this paper, we consider a non-autonomous stochastic LotkaVolterra competitive system dxi(t) = xi(t)[(bi(t)− n ∑ j=1 aij(t)xj(t))dt+σi(t)dBi(t)], where Bi(t) (i = 1, 2, · · · , n) are independent standard Brownian motions. Some dynamical properties are discussed and the sufficient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global at...

A novel coordinate transformation is used to reduce a simple generalization of the Lotka-Volterra dynamical system to a single second-order autonomous ordinary differential equation. Formal analytic solutions to this differential equation are presented which are shown to reduce to the recently obtained solution to the LotkaVolterra system [C. M. Evans and G. L. Findley, J. Math. Chem. 25 (1999)...

In this paper, we prove that the modified PainlevéInce (PI) equation, the force-free Duffing nonlinear type oscillator (DO) and the Lotka-Volterra (LV) nonlinear ordinary differential equation ODEs can be solved in general parametric form. The developed mathematical methodology and the extracted results, being expressed by way of new theorems including admissible functional transformations and ...

In this work we analyze the topological and dynamical properties of a simple model of complex food webs, namely the niche model. We describe the system as an oriented weighted graph and we assign a Lotka-Volterra population dynamics on the structure created by the niche model. After this we introduce “predators” and “prey” weighted graphs from which we underline patterns of competition among sp...