Abstract
The objective of this article is to study the significance of dynamical properties of non-autonomous deterministic as well as stochastic prey-predator model with Holling type-Ⅲ functional response. Firstly, uniform persistence of the deterministic model has been demonstrated. Secondly, stochastic non-autonomous prey-predator system with Holling type-Ⅲ functional response is proposed. The existence of a global positive solution has been derived. Sufficient conditions for non-persistence in mean, weakly persistence in mean, extinction have been derived. Moreover the sufficient conditions for permanence of the system have been established. The analytical results are verified by numerical simulation.
Highlights
The first major development in modern mathematical ecology was done when Lotka [26] and Volterra [36] published works for a predator-prey competing species
We have studied firstly the uniform persistence of the non-autonomous deterministic model of prey-predator population with Holling type-III functional response
We have thoroughly investigated the existence of global positive solution, persistence, permanence and extinction of the corresponding stochastic system
Summary
The first major development in modern mathematical ecology was done when Lotka [26] and Volterra [36] published works for a predator-prey competing species. Dynamical behavior of the ecological model system depends on the functional form of interaction between prey and predator representing the biological interaction in natural world. Among the many aspects of the prey-predator relationship, the key factor is the functional response. Functional response is defined as the intake rate of predator as a function of density of food. Nonlinear functional responses were originally proposed by Holling (1959) [13] on the basis of a general argument concerning the allocation of a predator’s time between two activities: prey searching and prey handling Holling considered predation of small mammals on pine sawflies and observed that predation rates increased with increasing prey population density. Holling type I functional response is noticed in passive predators like spiders. Death rate of prey due to predation is constant. Search rate of Holling type II is constant.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
