We study entire solutions of a two-component competition system with LotkaVolterra type nonlinearity in a lattice. It is known that this system has traveling wave front solutions and enjoys comparison principle. Based on these solutions, we construct some new entire solutions which behave as two traveling wave fronts moving towards each other from both sides of x-axis.

This paper considers the existence of positive almost-periodic solutions for almost-periodic LotkaVolterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

This paper is concerned with traveling wavefronts in a LotkaVolterra model with nonlocal delays for two cooperative species. By using comparison principle, some existence and nonexistence results are obtained. If the wave speed is larger than a threshold which can be formulated in terms of basic parameters, we prove the asymptotic stability of traveling wavefronts by the spectral analysis metho...

Some techniques of bilinearization of the non-autonomous 1 + 1 dimensional discrete soliton equations is discussed by taking the discrete KdV equation, the discrete Toda lattice equation, and the discrete LotkaVolterra equation as examples. Casorati determinant solutions to those equations are also constructed explicitly.

The qualitative behaviorof positive solutions of the neutral-delay two-species LotkaVolterra competitive system with several discrete delays is investigated. Sufficient conditions are obtained for the local asymptotic stability of the positive steady state. In fact, some of these sufficient conditions are also necessary except at those critical values. Results on the oscillatory and non-oscilla...

The current models developed in predictive microbiology to describe interactions between microflora in foods are reviewed, with a special focus on the Jameson-effect and LotkaVolterra approaches. One case-study is further explored: modelling the sparse growth of Listeria monocytogenes in diced bacon along the shelf-life.

We prove results that enable the efficient and natural realization of a large class of robust heteroclinic networks in coupled identical cell systems. We also propose some general conjectures that relate a natural and large class of robust heteroclinic networks that occur in networks modelled by equations of LotkaVolterra type, and certain networks of symmetric systems, to robust heteroclinic n...

In 1 , the general nonautonomous n-species Lotka-Volterra competitive systems with impulsive effects are investigated. By using the methods of inequalities estimate and constructing the suitable Liapunov functions, the sufficient conditions on the permanence of whole species and global attractivity of systems are established. In 2 , the authors studied the following general nonautonomous n-spec...

Hirota’s bilinear technique is applied to some integrable lattice systems related to the Bäcklund transformations of the 2DToda, Lotka-Volterra and relativistic LotkaVolterra lattice systems, which include the modified Lotka-Volterra lattice system, the modified relativistic Lotka-Volterra lattice system, and the generalized BlaszakMarciniak lattice systems. Determinant solutions are constructe...

In this paper we study the Gilpin-Ayala competition system with random perturbation which is more general and more realistic than the classical LotkaVolterra competition model. We verify that the positive solution of the system does not explode in a finite time. Furthermore, it is stochastically ultimately bounded and continuous a.s. We also obtain certain results about asymptotic behavior of t...