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Open AccessArticle

Diffusion Dynamics and Impact of Noise on a Discrete-Time Ratio-Dependent Model: An Analytical and Numerical Approach

1
Department of Mathematics, National Institute of Food Technology Entrepreneurship and Management, HSIIDC Industrial Estate, Kundli, Haryana 131028, India
2
School of Advanced Sciences, Department of Mathematics, VIT University, Vellore, Tamilnadu 632014, India
3
Department of Mathematics & Statistics, Aliah University, Action Area IIA/27, Newtown, Kolkata 700160, India
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(4), 103; https://doi.org/10.3390/mca24040103
Received: 22 November 2019 / Accepted: 12 December 2019 / Published: 17 December 2019
The paper deals with the dynamical behavior of a discrete-time ratio-dependent predator–prey system. The predator dependence is one of the main concerns of the system. The stability analysis of this 2-dimensional map was carried out analytically. Numerical simulation was carried out to verify the analytical results. We analyzed some specific features that could arise in discrete system. Basin of attraction was found for the endemic equilibrium state. We extended the numerical simulation for the maximal Lyapunov exponent. The presence of positive Lyapunov exponent indicated chaotic behavior of the map. The sensitive dependence on initial condition is one of the criteria for a discrete system. We showed that the system is sensitive on the initial conditions. We also carried out the analysis of diffusion and impact of noise. View Full-Text
Keywords: discrete ratio-dependent predator–prey model; stability; Hopf-bifurcation; Lyapunov exponent; sensitive dependence discrete ratio-dependent predator–prey model; stability; Hopf-bifurcation; Lyapunov exponent; sensitive dependence
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Das, K.; Srinivas, M.N.; Huda Gazi, N. Diffusion Dynamics and Impact of Noise on a Discrete-Time Ratio-Dependent Model: An Analytical and Numerical Approach. Math. Comput. Appl. 2019, 24, 103.

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