Related papers: Positive solutions to the reaction diffusion equat…
In this paper, we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment. It is known that Choi et al. [J. Differ. Equ. 302 (2021), pp. 807-853] studied the persistence or extinction…
We study the asymptotic behaviour near extinction of positive solutions of the Cauchy problem for the fast diffusion equation with a subcritical exponent. We show that separable solutions are stable in some suitable sense by finding a class…
A non-periodic version of the one-predator two-prey system model presented in [L.T.H. Nguyen, Q.H. Ta, T.V. T\d{a}, Existence and stability of periodic solutions of a Lotka-Volterra system, SICE International Symposium on Control Systems,…
Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
In this paper, we investigate so-called forced wave solutions of a three components reaction-diffusion system from population dynamics. Our system involves three species that are respectively two competing preys and one predator; moreover,…
In this work, the time-dependent solution for the Lotka-Volterra Predator-Prey model is derived with the help of the Lambert W function. This allows an exact analytical expression for the period of the associated limit-cycle oscillations…
A cubic discrete coupled logistic equation is proposed to model the predator-prey problem. The coupling depends on the population size of both species and on a positive constant $\lambda$, which could depend on the prey reproduction rate…
In a recent article the most general non-uniform reaction-diffusion models on a one-dimensional lattice with boundaries were considered, for which the time evolution equations of correlation functions are closed and the stationary profile…
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in $\mathbb{R}^d$. An important special case is the time-fractional diffusion equation, which has seen much…
The diffusion equation is extended by including spatial-temporal memory in such a manner that the conservation of the concentration is maintained. The additional memory term gives rise to the formation of non-trivial stationary solutions.…
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…
In models for the evolution of predation from initially purely competitive species interactions, the propensity of predation is most often assumed to be a direct consequence of the relative morphological and physiological traits of…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
Consider the coupling of $2$ evolution equations, each generating a global process. We prove that the resulting system generates a new global process. This statement can be applied to differential equations of various kinds. In particular,…
A predator prey system is investigated in this research, which is based on a modified version of the Leslie Gower scheme and a Holling-type II scheme with time dependent delays. Using Schauder's fixed point theorem, we studied the existence…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
Uniform-in-time bounds of nonnegative classical solutions to reaction-diffusion systems in all space dimension are proved. The systems are assumed to dissipate the total mass and to have locally Lipschitz nonlinearities of at most (slightly…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more…
In this paper, we proposed new predator-prey models that take into account memory and kicks. Memory is understood as the dependence of current behavior on the history of past behavior. The equations of these proposed models are…