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Complex dynamics near extinction in a predator-prey model with ratio dependence and Holling type III functional response
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posted on 2023-06-10, 06:06 authored by Konstantin BlyussKonstantin Blyuss, Yuliya KyrychkoYuliya Kyrychko, OB BlyussIn this paper, we analyze a recently proposed predator-prey model with ratio dependence and Holling type III functional response, with particular emphasis on the dynamics close to extinction. By using Briot-Bouquet transformation we transform the model into a system, where the extinction steady state is represented by up to three distinct steady states, whose existence is determined by the values of appropriate Lambert W functions. We investigate how stability of extinction and coexistence steady states is affected by the rate of predation, predator fecundity, and the parameter characterizing the strength of functional response. The results suggest that the extinction steady state can be stable for sufficiently high predation rate and for sufficiently small predator fecundity. Moreover, in certain parameter regimes, a stable extinction steady state can coexist with a stable prey-only equilibrium or with a stable coexistence equilibrium, and it is rather the initial conditions that determine whether prey and predator populations will be maintained at some steady level, or both of them will become extinct. Another possibility is for coexistence steady state to be unstable, in which case sustained periodic oscillations around it are observed. Numerical simulations are performed to illustrate the behavior for all dynamical regimes, and in each case a corresponding phase plane of the transformed system is presented to show a correspondence with stable and unstable extinction steady state.
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- Published
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Frontiers in Applied Mathematics and StatisticsISSN
2297-4687Publisher
Frontiers Media SAExternal DOI
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8Department affiliated with
- Mathematics Publications
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- Yes
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- Yes
Legacy Posted Date
2023-01-30First Open Access (FOA) Date
2023-01-30First Compliant Deposit (FCD) Date
2023-01-28Usage metrics
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