Numerical Analysis of Stability of Plant-Animal Interactions in Riparian Zones

Abstract

Ecological interactions of Plant, Animal Species, particularly in Riparian Zones have become a subject of intense interest in recent years. These Zones whether along a river bank or shore line, link dry and wet environments. These zones are biologically significant and study of Ecological models of Plant-Animal interactions in these zones help understand the myriad of factors at play there.

The authors of the present article, in their previous work have studied the interaction between a Plant and an Herbivorous mammal and the long term dynamics of their populations as Prey and Predator interactions. For this they closely followed the Lotka (1925)- Volterra (1931) model.

The interactions have been modeled as system of Ordinary Differential Equations from which the Equilibrium points are identified and the stability analysis of these points is carried out by Linear Stability analysis.

In this present work numerical estimates are presented for the stability analysis for the two species Eco system considered earlier. The equations of perturbation for each steady state are solved numerically using the MatLab command ‘ode45’ which employs Runge-Kutta method of 4th order for solving simultaneous differential equations. The numerical results have been given to MatLab command ‘plot’ to obtain a graphical representation of the same. Criteria for the asymptotic stability of the states have been noted.