2. Consider the nonlinear system of differential equations dx = r*y – xy dt dy = y – e" dt (a) Determine all critical points of the system. (b) For each critical point not on the y-axis: i. Determine the linearisation of the system with the critical point translated to (0,0) and discuss whether it can be used to approximate the behaviour of the non-linear system. ii. Find the general solution of the linearised system using eigenvalues and eigenvectors.

2. Consider the nonlinear system of differential equations dx = r*y – xy dt dy = y – e" dt (a) Determine all critical points of the system. (b) For each critical point not on the y-axis: i. Determine the linearisation of the system with the critical point translated to (0,0) and discuss whether it can be used to approximate the behaviour of the non-linear system. ii. Find the general solution of the linearised system using eigenvalues and eigenvectors.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 10EQ: In Exercises 1-12, find the solution of the differential equation that satisfies the given boundary...

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