Digital Repository

Analysis of a stochastic predator-prey model

Show simple item record Prasadini, K.D.S. Mallawa Arachchi, D.K. 2017-07-21T08:17:57Z 2017-07-21T08:17:57Z 2016
dc.identifier.citation Prasadini, K.D.S. and Mallawa Arachchi, D.K. 2016. Analysis of a stochastic predator-prey model. In Proceedings of the International Research Symposium on Pure and Applied Sciences (IRSPAS 2016), Faculty of Science, University of Kelaniya, Sri Lanka. p 57. en_US
dc.identifier.isbn 978-955-704-008-0
dc.description.abstract In biological systems Lotka-Volterra predator-prey model describes the population dynamics of two interacting species of predators and its preys. Classical predatorprey model is a primitive deterministic model governed by the two differential equations, namely, ���� = (������ − ��������) ���� and ���� = (�������� − ������) ���� where �� and �� denote prey and predator respectively, and ����, ����, ���� and ���� are parameters. This model can be improved by introducing stochasticity that accounts for the random fluctuations of a realistic predator-prey dynamical system. In this research work, we use Stochastic Differential Equation (SDE) approach. There are various ways, based on various assumptions, to incorporate SDE. One common approach is to use equations of the following form: ���� = (������ − ��������) ���� + ��(���� + ����)�� ������ ���� = (�������� − ������) ���� + ��(���� + ����)�� ������ These types of Stochastic Differential Equations (SDE) can be simulated in Matlab using numerical methods such as Euler-Maruyama method. Phase planes of the deterministic and stochastic models are carried out to demonstrate the behavior of this modified model. Our initial goal is to compare different stochastic models with the original deterministic model through simulations. The deterministic model has a positive equilibrium which is globally stable for positive values of the parameters. Nevertheless, in the stochastic model, the predator and prey populations may tend to extinction. Extinction percentages of predator or prey population are summarized and analyzed through this research work. en_US
dc.language.iso en en_US
dc.publisher Faculty of Science, University of Kelaniya, Sri Lanka en_US
dc.subject Predator-prey model en_US
dc.subject Stochastic differential equations en_US
dc.subject Matlab simulations en_US
dc.title Analysis of a stochastic predator-prey model en_US
dc.type Article en_US

Files in this item

This item appears in the following Collection(s)

Show simple item record

Search Digital Repository


My Account