# Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes

Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes A mathematical model of predator–prey system is studied analytically as well as numerically. The objective of this paper is to study systematically the dynamical properties of a modified Leslie–Gower predator–prey model with Holling type III functional response. We discuss different types of system behaviours for various parameter values. The essential mathematical features of the model with regard to the boundedness, stability and persistence have been carried out. Some numerical simulations are carried out to support our theoretical analysis. All the results are expected to be of use in the study of the dynamic complexity of ecosystem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Modeling Earth Systems and Environment Springer Journals

# Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes

, Volume 4 (2) – Mar 28, 2018

## Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes

A mathematical model of predator–prey system is studied analytically as well as numerically. The objective of this paper is to study systematically the dynamical properties of a modified Leslie–Gower predator–prey model with Holling type III functional response. We discuss different types of system behaviours for various parameter values. The essential mathemati- cal features of the model with regard to the boundedness, stability and persistence have been carried out. Some numerical simulations are carried out to support our theoretical analysis. All the results are expected to be of use in the study of the dynamic complexity of ecosystem. Keywords Modified Lesli–Gower model · Equilibria · Boundedness · Stability · Persistence Mathematics Subject Classification 92Bxx · 92D30 · 92D40 · 37B25 · 34D23 Introduction dx =(a − b x)x − p(x)y, (1a) 1 1 dt The dynamical behaviours between different populations and their complex properties have been examined by biologists dy y and ecologists. Following Lotka Volterra’s famous work = a − n y, (1b) dt x on population dynamics, numerous mathematical models have been performed to study the relation between predator x(0) ≥ 0, y(0) ≥ 0, population and prey population. The predator–prey model where still continues to be used in investigating the dynamics of interacting populations. In recent times, predator–prey sys- 1. x(t) and y(t) stand for population (the density) of the prey tem is one of the most important fields of interest. Many and predator at time t respectively, researchers have tried several approaches to study this inter- 2. a and a are the intrinsic growth rates of prey and preda- esting field. Two species Leslie–Gower predator–prey model 1 2 tor respectively, was introduced by Leslie (1948, 1958). Two species Les- 3. b measures the strength of...

/lp/springer_journal/study-of-a-predator-prey-model-with-modified-leslie-gower-and-holling-bnlzBfCO1I
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Earth Sciences; Earth System Sciences; Math. Appl. in Environmental Science; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Mathematical Applications in the Physical Sciences; Ecosystems; Environment, general
ISSN
2363-6203
eISSN
2363-6211
D.O.I.
10.1007/s40808-018-0441-1
Publisher site
See Article on Publisher Site

### Abstract

A mathematical model of predator–prey system is studied analytically as well as numerically. The objective of this paper is to study systematically the dynamical properties of a modified Leslie–Gower predator–prey model with Holling type III functional response. We discuss different types of system behaviours for various parameter values. The essential mathematical features of the model with regard to the boundedness, stability and persistence have been carried out. Some numerical simulations are carried out to support our theoretical analysis. All the results are expected to be of use in the study of the dynamic complexity of ecosystem.

### Journal

Modeling Earth Systems and EnvironmentSpringer Journals

Published: Mar 28, 2018

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