On a three-tier ecological food chain model with deterministic and random harvesting: A mathematical study
Articles
B. Mukhopadhyay
Central Calcutta Polytechnic, India
R. Bhattacharyya
The Calcutta Technical School, India
Published 2011-01-25
https://doi.org/10.15388/NA.16.1.14116
PDF

Keywords

autotroph
herbivore
harvesting
poaching
wildlife management
noise
mean square stability

How to Cite

Mukhopadhyay, B. and Bhattacharyya, R. (2011) “On a three-tier ecological food chain model with deterministic and random harvesting: A mathematical study”, Nonlinear Analysis: Modelling and Control, 16(1), pp. 77–88. doi:10.15388/NA.16.1.14116.

Abstract

In the present study, we consider a nutrient-autotroph-herbivore ecosystem model where the herbivore species is assumed to have a commercial value. We use a Holling type-II harvest function to model density dependent herbivore harvesting. Stability criteria of the resulting model is investigated both from analytical and numerical viewpoints. The investigation revealed the existence of a number of threshold values of the harvest rate that have a remarkable influence on the system dynamics. Next we incorporate a noise term in the parameter representing harvest rate to model the phenomenon of poaching as random harvesting. The stochastic model is analyzed for exponential mean square stability and the resulting criteria in terms of harvest related parameters obtained. These parameter thresholds could be utilized to develop effective harvesting strategies and wildlife management policies which take into account the overall survival of the ecological populations.

PDF

Downloads

Download data is not yet available.