Question

• (Problem 2) Consider the second version of the Lotka-Volterra model: F(a – bF – cS) dF dt ds dt S(-k + \F). (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b, c, k, 1. Plot the solutions of the model and the phase portrait including trajectories near the equilibrium points.

Answer 1

Lotka-Volterra model is the simplest model of predator-prey interactions. The model was developed independently by Lotka (1925) and Volterra (1926)

for the given equations,

F=density of prey

S=density of predators

a=intrinsic rate of prey population increase

b=efficiency of prey changing to predator

c=prediction rate coefficient

lamda=reproduction rate of predators per 1 prey eaten

k=predator mortality rate

It forms the basis of many models used today in the analysis of population dynamics. Unfortunately, in its original form Lotka-Volterra has some significant problems