3. Two species with population sizes x and y evolve according to the following pair of coupled differential equations: dx = 4x(5- y), dt dy dt =-y(1-x). I (a) [ (b) (c) (d) Briefly explain what kind of system these equations describe and provide an inter- pretation for each of the various terms in these equations. 1 Determine all of the equilibrium points for x, y. Find an approximate solution to these equations near to non-zero equilibrium. Describe the general behaviour of x, y in the four regions I: x1, y <5, II: >1,y>5 III: <1,y> 5, IV: x < 1, y < 5.

3. Two species with population sizes x and y evolve according to the following pair of coupled differential equations: dx = 4x(5- y), dt dy dt =-y(1-x). I (a) [ (b) (c) (d) Briefly explain what kind of system these equations describe and provide an inter- pretation for each of the various terms in these equations. 1 Determine all of the equilibrium points for x, y. Find an approximate solution to these equations near to non-zero equilibrium. Describe the general behaviour of x, y in the four regions I: x1, y <5, II: >1,y>5 III: <1,y> 5, IV: x < 1, y < 5.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

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