On the Dynamics of a Discrete Predator–Prey Model

Priyanka Saha, Nandadulal Bairagi () and Milan Biswas
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Priyanka Saha: Jadavpur University, Centre for Mathematical Biology and Ecology, Department of Mathematics
Nandadulal Bairagi: Jadavpur University, Centre for Mathematical Biology and Ecology, Department of Mathematics
Milan Biswas: A. J. C. Bose College

A chapter in Trends in Biomathematics: Modeling, Optimization and Computational Problems, 2018, pp 219-232 from Springer

Abstract: Abstract We here discretize a predator–prey model by standard Euler forward method and non-standard finite difference method and then compare their dynamic properties with the corresponding continuous-time model. We show that NSFD model preserves positivity of solutions and is completely consistent with the dynamics of the corresponding continuous-time model. On the other hand, the discrete model formulated by forward Euler method does not show dynamic consistency with its continuous counterpart. Rather it shows scheme-dependent instability when step-size restriction is violated.

Keywords: Discrete Predator-prey Model; Nonstandard Finite Difference (NSFD); Forward Euler Method; Dynamic Consistency; Step Size Restriction (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-91092-5_15

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DOI: 10.1007/978-3-319-91092-5_15

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