Existence of global solutions for a predator-prey model with cross-diffusion.
Existence of global solutions for a system of reaction-diffusion equations having a triangular matrix.
Existence of limit cycles in a predator-prey system with a functional response.
Existence of periodic solutions for a delayed ratio-dependent three-species predator-prey diffusion system on time scales.
Existence of periodic solutions of a delayed predator-prey system on time scales.
Existence of positive periodic solutions for a class of nonautonomous difference equations.
Existence of positive periodic solutions for delayed predator-prey patch systems with stocking.
Existence of positive periodic solutions of an SEIR model with periodic coefficients
An SEIR model with periodic coefficients in epidemiology is considered. The global existence of periodic solutions with strictly positive components for this model is established by using the method of coincidence degree. Furthermore, a sufficient condition for the global stability of this model is obtained. An example based on the transmission of respiratory syncytial virus (RSV) is included.
Existence of solutions to generalized von Foerster equations with functional dependence
We prove the existence of solutions to a differential-functional system which describes a wide class of multi-component populations dependent on their past time and state densities and on their total size. Using two different types of the Hale operator, we incorporate in this model classical von Foerster-type equations as well as delays (past time dependence) and integrals (e.g. influence of a group of species).
Existence of Waves for a Nonlocal Reaction-Diffusion Equation
In this work we study a nonlocal reaction-diffusion equation arising in population dynamics. The integral term in the nonlinearity describes nonlocal stimulation of reproduction. We prove existence of travelling wave solutions by the Leray-Schauder method using topological degree for Fredholm and proper operators and special a priori estimates of solutions in weighted Hölder spaces.
Existence, uniqueness and ergodicity of positive solution of mutualism system with stochastic perturbation.
Explicit solutions of Fisher's equation with three zeros.
Extinction in a generalized Lotka-Volterra predator-prey model.
Extinction in nonautonomous discrete Lotka-Volterra competitive system with pure delays and feedback controls.
Extinction in nonautonomous Kolmogorov systems
We consider nonautonomous competitive Kolmogorov systems, which are generalizations of the classical Lotka-Volterra competition model. Applying Ahmad and Lazer's definitions of lower and upper averages of a function, we give an average condition which guarantees that all but one of the species are driven to extinction.
Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances
A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]....