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Written from an original, engineering point of view, this volume presents a general nonlinear theory concerning the stability, instability, bifurcation, and oscillatory behavior of autonomous systems. Huseyin stresses analytical procedures which lead to construction of asymptotic solutions. He analyzes various bifurcation phenomena and the associated imperfection-sensitivities via the multiple-parameter perturbation technique, a method which generates distinct forms of equilibrium surfaces linked to "elementary catastrophes." In addition, he introduces an intrinsic harmonic balancing technique to analyze the dynamic bifurcations, resulting in a unified treatment of both static and dynamic bifurcation phenomena within an autonomous framework. Throughout the work, the presentation is conceptually simple and practical.

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CONTENTS
1 INTRODUCTION = 1
 1.1 Introductory remarks = 1
 1.2 Modelling of reality = 4
 1.3 Mathematical formulation and basic definitions = 7
 1.4 stability in autonomous systems = 12
 1.5 Autonomous systems with parameters = 23
 1.6 Classification of autonomous systems = 26
2 POTENTIAL SYSTEMS = 35
 2.1 Potential function and stability of equilibrium states = 35
 2.2 Classification of critical conditions = 41
 2.3 Equilibrium surface via the multiple-parameter perturbation technique = 43
  2.3.1 Regular (non-critical) equilibrium states = 43
  2.3.2 General critical points = 44
 2.4 Simple general points and elementary catastrophes = 48
  2.4.1 General points of order 2 = 48
  2.4.2 General points of order 3 (singular geneeal point) = 52
  2.4.3 General points of order 4 and higher order = 56
 2.5 Two-fold general critical points = 57
  2.5.1 Equilibrium surface and connection with umbilics = 57
  2.5.2 Critical zone = 60
 2.6 Special critical points and imperfection sensitivity = 62
 2.7 Concluding remdrks = 77
3 STATIC INSTABILiTY OF AUTONOMOUS SYSTEMS = 79
 3.1 One-parameter systems = 79
  3.1.1 Simple critical points (divergence) = 83
  3.1.2 Simple bifurcation points = 92
  3.1.3 Stability of equilibrium paths in the vicinity of simple bifurcation points = 100
  3.1.4 Compound branching = 106
  3.1.5 Imperfection sensitivity of critical points = 110
 3.2 Multiple-parameter systems = 122
  3.2.1 Classifiation of critical points = 122
  3.2.2 Simple general points of order 2 = 123
  3.2.3 Simple general points of order 3 (singular general points) = 135
  3.2.4 Compound general points = 141
  3.2.5 Special critical points = 144
 3.3 Concluding remarks = 154
4 DYINAMIC INSTABILITY OF AUTONOMOUS SYSTEMS = 156
 4.1 Introductory remarks = 156
 4.2 Non-linear oscillations and the method of harmonic balancing = 157
 4.3 An intrinsic method of harmonic analysis = 161
 4.4 One-parameter systems = 167
  4.4.1 Hopf bifurcation = 167
  4.4.2 An illustrative example = 179
  4.4.3 Flat Hopf bifurcation = 182
  4.4.4 Symmetric bifurcation (tri-furcation) = 183
 4.5 Alternative formulation of one-parameter systems = 188
  4.5.1 Double Hopf bifurcation = 192
  4.5.2 Cusp bifurcation = 196
  4.5.3 Tangential bifurcation = 200
 4.6 Stability of limit cycles = 203
  4.6.1 Hopf bifurcation = 206
  4.6.2 symmetric bifurcation (tri-furcation) = 207
 4.7 Multiple-parameter systems = 208
  4.7.1 Generalized Hopf bifurcation No. 1 = 211
  4.7.2 Generalized Hopf bifurcation No. 2 = 214
  4.7.3 Generalized Hopf bifurcation No. 3 = 218
  4.7.4 More generalized bifurcations = 219
 4.8 Concluding remarks = 223
5 APPLICATIONS = 225
 5.1 Potential systems in mechanics = 225
  5.1.1 A structural model = 225
  5.1.2 Columns on elastic foundations = 229
  5.1.3 Experimental results = 232
 5.2 Autonomous mechanical and electrical systems = 233
  5.2.1 A mechanical system = 234
  5.2.2 Static instability of a non-linear network = 237
  5.2.3 Hopf bifurcation associated with a non-linear network = 239
  5.2.4 A mechanical system and its electrical analogue = 242
 5.3 Thermodynamics: phase Transitions = 250
 5.4 Bio-chemical processes (static instability) = 251
 5.5 The Brusselator = 253
 5.6 Aircraft at high angles of attack = 257
 5.7 Urban systems = 259
6 CONCLUDING REMARKS = 262
APPENDIX = 267
REFERENCES = 270
INDEX = 279