A First Course in the Qualitative Theory of Differential Equations

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Prentice Hall, 2003 - Mathematics - 558 pages
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This book provides a complete analysis of those subjects that are of fundamental importance to the qualitative theory of differential equations and related to current research—including details that other books in the field tend to overlook. Chapters 1—7 cover the basic qualitative properties concerning existence and uniqueness, structures of solutions, phase portraits, stability, bifurcation and chaos. Chapters 8—12 cover stability, dynamical systems, and bounded and periodic solutions. A good reference book for teachers, researchers, and other professionals.

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Contents

Stability Part I
221
Linear Equations with Constant Coefficients
229
Perturbations on Linear Equations
236
Linear Equations with Periodic Coefficients
243
Liapunovs Method for Autonomous Equations
250
Some Applications
265
Bifurcation
272
SaddleNode Bifurcation
285
Chaos
317
Maps and Their Bifurcations
324
Route to Chaos
336
Universality
356
The Lorenz System and Strange Attractors
361
The Smale Horseshoe
370
Dynamical Systems
378
PoincaréBendixson Theorem in ÎÎ2
380

Transcritical Bifurcation
293
Pitchfork Bifurcation
297
PoincaréAndronovHopf Bifurcation
312
Limit Cycles
400
LotkaVolterra Equation
413
Manifolds and the HartmanGrobman Theorem
418

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About the author (2003)

Liu has been lecturing in psychology at Victoria University, Wellington since 1994.

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