In:
Journal of Biological Systems, World Scientific Pub Co Pte Ltd, Vol. 32, No. 02 ( 2024-06), p. 585-603
Abstract:
An ecosystem with anti-predator behavior is established in both deterministic and stochastic environments. This means that adult prey could attack weak predators. Bifurcation diagrams are used to analyze the deterministic case, while a tool called the most probable trajectory, defined by the spatial extreme point of the probability density function (PDF), is employed to explore the stochastic case. The Fokker-Planck equation is solved using the stochastic averaging method of energy envelope, which provides an analytical expression for the PDF. The results show that in the deterministic case, effective anti-predator behavior can dampen predator-prey oscillations and mitigate negative effects caused by the time delay. Additionally, it can accelerate the transient solution to reach a steady state and reduce the ratio of predator-to-prey densities in coexistence. In the stochastic case, effective anti-predator behavior can raise the noise threshold that leads to population extinction. Furthermore, it can also reduce the randomness of solutions. It’s worth noting that appropriate anti-predator behavior can ensure that the most probable solution in the stochastic system approximates the solution in the deterministic system. Monte Carlo simulations verify the accuracy of these analytical results.
Type of Medium:
Online Resource
ISSN:
0218-3390
,
1793-6470
DOI:
10.1142/S0218339024500219
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2024
detail.hit.zdb_id:
2026740-X
SSG:
12
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