Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations

Front Cover
Cambridge University Press, Nov 25, 1994 - Mathematics - 388 pages
By providing an introduction to nonlinear differential equations, Dr. Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems.
 

Selected pages

Contents

I
xi
II
2
III
8
V
9
VI
15
VII
19
VIII
21
IX
26
LVII
170
LIX
173
LX
174
LXI
175
LXII
178
LXIII
182
LXIV
186
LXV
188

X
34
XI
40
XII
41
XIII
44
XIV
45
XV
48
XVI
49
XVII
51
XVIII
60
XIX
63
XX
64
XXI
67
XXII
71
XXIII
72
XXV
77
XXVI
83
XXVII
84
XXVIII
86
XXIX
90
XXX
94
XXXI
96
XXXII
103
XXXIII
113
XXXIV
118
XXXV
120
XXXVI
123
XXXVII
124
XXXVIII
126
XL
131
XLI
135
XLII
139
XLIII
140
XLIV
144
XLV
145
XLVI
150
XLIX
151
L
152
LI
155
LII
156
LIII
159
LIV
164
LV
166
LXVI
191
LXVIII
193
LXIX
198
LXX
200
LXXI
205
LXXII
207
LXXIII
211
LXXIV
214
LXXVI
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LXXVII
230
LXXVIII
236
LXXIX
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LXXX
241
LXXXII
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LXXXIII
247
LXXXIV
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LXXXV
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LXXXVI
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LXXXVII
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XC
268
XCI
270
XCII
271
XCIII
277
XCIV
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XCVI
285
XCVII
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XCVIII
294
XCIX
305
C
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CI
314
CII
317
CIII
326
CIV
327
CV
332
CVI
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CVII
339
CVIII
353
CIX
359
CX
363
CXI
366
CXII
370
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Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear ...
Paul Glendinning
No preview available - 1994

Common terms and phrases

A-graph a₁ asymptotically stable behaviour bifurcation theory centre manifold change of coordinates chaotic chapter coefficients consider defined definition differential equation e₁ eigenvalues eigenvectors example EXERCISE exists f-covers fixed point Floquet multipliers gives Hence homoclinic bifurcations homoclinic orbit Hopf bifurcation hyperbolic stationary point I₁ initial conditions interval invariant Jacobian matrix Lemma Liapounov function Liapounov stable linear map Manifold Theorem neighbourhood node non-hyperbolic nonlinear terms normal form obtain orbit of period origin oscillator period-doubling bifurcation periodic orbit periodic solutions phase portrait phase space plane Poincaré-Bendixson Theorem points of period proof prove region resonant return map saddle saddlenode bifurcation shown in Figure simple stable manifold theorem stationary point sufficiently small Suppose T₁ tangential tend terms of order trajectories transcritical bifurcation unimodal maps unstable manifold whilst x₁ Xn+1 zero μα μη

References to this book

Bibliographic information

TitleStability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations
Cambridge Texts in Applied Mathematics
AuthorPaul Glendinning
Editionillustrated, reprint
PublisherCambridge University Press, 1994
ISBN0521425662, 9780521425667
Length388 pages
Subjects ›  › 

Mathematics / Differential Equations / General
Mathematics / General
Science / Chaotic Behavior in Systems
  
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