Bifurcation and Stability of Steady Solutions of Evolution Equations

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ABSTRACT We considered the evolutional problems in two-dimensional autonomous system. We showed that the bifurcating steady solutions are obtained from the points of intersection of the two conic sections and we used the implicit function theorem to justify their existence, and also we applied the Lyapunov theorem to establish their stability.

CONTENTS

Title Page i

Certification ii

Dedication iii

Acknowledgement iv

Contents v

Abstract vi

Chapter One INTRODUCTION 1

Chapter Two LITERATURE REVIEW 6

Chapter Three STABILITY OF LINEAR SYSTEMS 12

Chapter Four BIFURCATION AND STABILITY OF STEADY

SOLUTIONS OF EVOLUTION EQUATIONS 28

Chapter Five FURTHER WORK ON BIFURCATION AND

STABILITY 43

CONCLUSION 48

APPENDIX 49

REFERENCES 56


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