Prove non-existence of limit cycles for the system i = y? – x, ý = -y + 2xy + 2y by a) using index theory, b) showing that it is a gradient system, and c) using Dulac's criterion (Hint: you can choose g = 1/y).

Prove non-existence of limit cycles for the system i = y? – x, ý = -y + 2xy + 2y by a) using index theory, b) showing that it is a gradient system, and c) using Dulac's criterion (Hint: you can choose g = 1/y).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 12EQ

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Question

Prove non-existence of limit cycles for the system
å = y? – x, ý = -y³ + 2xy + 2y
by
a)
using index theory,
b)
showing that it is a gradient system, and
c)
using Dulac's criterion (Hint: you can choose g = 1/y).

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