The environmental effect on dynamics of the competition model with herd behavior

Miljana Stanković; Miljana Jovanović

doi:10.3934/dcdsb.2022239

Article Contents

2023, Volume 28, Issue 6: 3747-3767. Doi: 10.3934/dcdsb.2022239

This issue Previous Article An overview on deep learning-based approximation methods for partial differential equations Next Article Well-posedness and dynamic properties of solutions to a class of fourth order parabolic equation with mean curvature nonlinearity

The environmental effect on dynamics of the competition model with herd behavior

Miljana Stanković^1, and
Miljana Jovanović^1, ,

1.
University of Niš, Faculty of Sciences and Mathematics, Serbia

^*Corresponding author: Miljana Jovanović
^*Corresponding author: Miljana Jovanović

Received: December 2021

Revised: October 2022

Early access: December 2022

Published: June 2023

The second author is supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, No. 451-03-68/2022-14/200124

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Abstract

In this paper, the competition model with herd behavior and the Allee effect, which dynamics is described by the two-dimensional system of stochastic differential equations, is considered. We verify that the environmental noise included in the model provides a solution that is positive, global and bounded. Conditions under which the system is stable in some sense are presented. Finally, as an illustration, we apply our mathematical results for the prediction of time for which populations of the Asiatic black bear (Ursus thibetanus) and wild boar (Sus scrofa) in the Mount Jiri National Park, need to reach their equilibrium state.

Keywords:

Mathematics Subject Classification: Primary: 60H10, 60H35; Secondary: 92D25, 92D40, 34F05.

Citation:

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Figure 1. The mean value of $ 33 $ stochastic trajectories of the system (2) and real data for Asiatic black bear population

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Figure 2. The mean values of twenty stochastic trajectories of the system (2) with the parameters (29), when $ \alpha_0 = 100, \, \beta_0 = 4 $ and $ \alpha_0 = 100, \, \beta_0 = 35 $

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Figure 3. Deterministic and twenty stochastic trajectories of the system (2) with the parameters (30)

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