On a periodic mutualism model

Almost Periodic Solutions of a Discrete Mutualism Model with Variable Delays

We discuss a discrete mutualism model with variable delays of the forms N1 n 1 N1 n exp{r1 n K1 n α1 n N2 n − μ2 n /1 N2 n − μ2 n − N1 n − ν1 n }, N2 n 1 N2 n exp{r2 n K2 n α2 n N1 n − μ1 n / 1 N1 n − μ1 n − N2 n − ν2 n }. By means of an almost periodic functional hull theory, sufficient conditions are established for the existence and uniqueness of globally attractive almost periodic solution ...

Almost Periodic Solutions of a Discrete Mutualism Model with Feedback Controls

Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism

Mutualism is the interaction of two species of organisms that benefits both [1]. In general, mutualism may be either obligate or facultative. Obligatemutualistmay survive only by association, and facultative mutualist, while benefiting from the presence of each other, may also survive in the absence of any of them [2]. As it is well known, in recent years the nonautonomous and periodic populati...

Multiplicity of Almost Periodic Oscillations in a Harvesting Mutualism Model with Time Delays

By means of Mawhin’s continuation theorem of coincidence degree theory, some new sufficient conditions are obtained for the existence of at least four positive almost periodic solutions for a harvesting mutualism model with time delays. To the best of the author’s knowledge, so far, the result of this paper is completely new. An example is employed to illustrate the result of this paper.

Positive periodic solutions of a discrete mutualism model with time delays

where ri,Ki,αi ∈ C(R,R+), αi > Ki, i = 1,2, τi,σi ∈ C(R,R+), i = 1,2, ri, Ki, αi, τi, σi(i = 1,2) are functions of period ω > 0. Since the study on periodic solutions of a population model is of great interest in mathematical biology [5] and many authors [1, 7] have argued that the discrete-time models governed by difference equations are more appropriate than the continuous ones when the popul...