Question

1. Consider the Lotka-Volterra model for the interaction between a predator population (wolves W(t)) and a prey population (moose M(t)), À = aM - bmw W = -cW+dMW with the four constants all positive. (a) Explain the meaning of the terms. (b) Non-dimensionalize the equations in the form dx/dt = *(1 - y) and dy/dt = xy(x - 1). (c) Find the fixed points, linearize, classify their stability and draw a phase diagram for various initial conditions (again, using a computer is fine). You should find a center. Can you trust that this is really a center?

Answer 1

Thus, the prey equation could be explained an follow :- The rate of change of the prey's population is given by it't own goowth minua the rate at which it in preyed upon. Explanation of predator equation in dw = amw-cms IT qmw representa the growth of the predator population 'CW represent the loss rate of the predotoon due to either natural death on emigration, it lead to an exponential decay in the absence of prey. Hence the equation exprenen that the rate of change of the predator's population depend upon the date at which consumer prey Minna it intonac death sate. A linearization of the equation yield, a solution similar to Simple harmonic motion with the population of predatorn training that of prey by qot 90° in the cycle. botoinded - predator Time Scanned with CamScanner