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Research Journal of Pharmacy and Technology
Year : 2016, Volume : 9, Issue : 11
First page : ( 1892) Last page : ( 1901)
Print ISSN : 0974-3618. Online ISSN : 0974-360X.
Article DOI : 10.5958/0974-360X.2016.00388.7

Effect of white noise and diffusion on the dynamics of predator-prey density dependent model

Reddy K. Shiva1,*, Kumar C.V. Pavan2,**, Srinivas M. N.3,***, Srinivas M. A. S.4,****

1Department of Mathematics, Anurag Group of Institutions, Venkatapur, Hyderabad-500 088, India

2Department of Mathematics, Vignan Institute of Technology and Science, Vignan Hills, Hyderabad, India

3School of Advanced Sciences, VIT University, Vellore-632 014, India

4Department of Mathematics, Jawaharlal Nehru Technological University, Kukatpally, Hyderabad

*Corresponding Author E-mail: shivareddy.konda@gmail.com

**cheruvu.pavankumar76@gmail.com

***mnsrinivaselr@gmail.com

****massrinivas@gmail.com

Online published on 2 March, 2017.

Abstract

In this paper, we consider an ecological model consisting of prey and predator along with special effect of diffusion and random perturbations. The Routh-Hurwitz principle and Lyapunov's function are employed to analyze the local and global stability of the system respectively, without delay and diffusion, around the positive equilibrium point. The stability of the system is analyzed with delay and without diffusion. Diffusive instability is also verified by perturbation technique and Routh-Hurwitz criteria. The analytical estimates of the meansquare fluctuation of population have also been calculated to explore the dynamics of the system in the presence of Gaussian additive white noise. Computer simulations through MATLAB have been carried out to illustrate the analytical results with suitable numerical examples.

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Keywords

Stability, Lyapunov function, time delay, limit cycles, diffusion, random noise.

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