K. Shiva Reddy, C.V. Pavan Kumar, M. N. Srinivas, M. A. S. Srinivas
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K. Shiva Reddy1*, C.V. Pavan Kumar2, M. N. Srinivas3, M. A. S. Srinivas4
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.
Volume - 9,
Issue - 11,
Year - 2016
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 mean-square 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.
Cite this article:
K. Shiva Reddy, C.V. Pavan Kumar, M. N. Srinivas, M. A. S. Srinivas. Effect of white noise and Diffusion on the dynamics of predator- prey density dependent model. Research J. Pharm. and Tech 2016; 9(11):1892-1901. doi: 10.5958/0974-360X.2016.00388.7