Abstract
This article is concerned with a mutualism ecological model with Lévy noise. The local existence anduniqueness of a positive solution are obtained with positive initial value, and the asymptotic behaviorto the problem is studied. Moreover, we show that the solution is stochastically bounded and stochastic permanence.The sufficient conditions for the system to be extinct are given and the conditions for the systemto be persistence in mean are also established.
Highlights
Mutualism is an important biological interaction in nature. It occurs when one species provides some benefit in exchange for some benefit, for example, pollinators and flowering plants, the pollinators obtain floral nectar as a food resource while the plant obtains non-trophic reproductive benefits through pollen dispersal and seed production
Another instance is ants and aphids, in which the ants obtain honeydew food resources excreted by aphids while the aphids obtain increased survival by the non-trophic service of ant defense against natural enemies of the aphids
In the description of population dynamics, it is critical to discuss the property of persistence in mean and extinction
Summary
Mutualism is an important biological interaction in nature. It occurs when one species provides some benefit in exchange for some benefit, for example, pollinators and flowering plants, the pollinators obtain floral nectar (and in some cases pollen) as a food resource while the plant obtains non-trophic reproductive benefits through pollen dispersal and seed production. ), and a unique positive interior equilibrium point E∗ = (x∗, y∗) satisfying the following equations r1. Lots of authors introduced stochastic perturbation into deterministic models to reveal the effect of environmental variability on the population dynamics in mathematical ecology [8, 11, 18, 17, 16, 21, 25, 26, 27, 34, 35]. The global existence and uniqueness of the positive solution to problem (1.4) are proved by using comparison theorem for stochastic equations. The problem of (1.5) is said to be persistence in mean
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