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Time-delayed and stochastic effects in a predator-prey model with ratio dependence and Holling type III functional response
journal contribution
posted on 2023-06-10, 01:18 authored by Konstantin BlyussKonstantin Blyuss, S N Kyrychko, Yuliya KyrychkoYuliya KyrychkoIn this article, we derive and analyze a novel predator-prey model with account for maturation delay in predators, ratio dependence, and Holling type III functional response. The analysis of the system’s steady states reveals conditions on predation rate, predator growth rate, and maturation time that can result in a prey-only equilibrium or facilitate simultaneous survival of prey and predators in the form of a stable coexistence steady state, or sustain periodic oscillations around this state. Demographic stochasticity in the model is explored by means of deriving a delayed chemical master equation. Using system size expansion, we study the structure of stochastic oscillations around the deterministically stable coexistence state by analyzing the dependence of variance and coherence of stochastic oscillations on system parameters. Numerical simulations of the stochastic model are performed to illustrate stochastic amplification, where individual stochastic realizations can exhibit sustained oscillations in the case, where deterministically the system approaches a stable steady state. These results provide a framework for studying realistic predator-prey systems with Holling type III functional response in the presence of stochasticity, where an important role is played by non-negligible predator maturation delay.
History
Publication status
- Published
File Version
- Accepted version
Journal
ChaosISSN
1054-1500Publisher
American Institute of PhysicsExternal DOI
Issue
7Volume
31Article number
a073141Event location
United StatesDepartment affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2021-10-06First Open Access (FOA) Date
2021-10-06First Compliant Deposit (FCD) Date
2021-10-05Usage metrics
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