## Nonlinear Differential Equations and Dynamical SystemsFor lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal. Its excellent pedagogical style typically consists of an insightful overview followed by theorems, illustrative examples, and exercises. |

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### Contents

I | 1 |

II | 3 |

III | 4 |

IV | 7 |

VI | 10 |

VII | 14 |

VIII | 16 |

IX | 21 |

LV | 136 |

LVI | 138 |

LVII | 140 |

LVIII | 144 |

LIX | 147 |

LX | 150 |

LXI | 154 |

LXII | 157 |

X | 23 |

XI | 25 |

XIII | 29 |

XIV | 31 |

XV | 36 |

XVI | 38 |

XVIII | 40 |

XIX | 43 |

XX | 47 |

XXI | 53 |

XXII | 57 |

XXIII | 59 |

XXIV | 61 |

XXV | 62 |

XXVI | 66 |

XXVII | 67 |

XXVIII | 69 |

XXX | 71 |

XXXI | 75 |

XXXII | 80 |

XXXIII | 83 |

XXXV | 88 |

XXXVI | 91 |

XXXVII | 93 |

XXXVIII | 96 |

XXXIX | 98 |

XL | 103 |

XLI | 107 |

XLII | 108 |

XLIII | 110 |

XLV | 113 |

XLVI | 116 |

XLVII | 119 |

XLVIII | 120 |

XLIX | 122 |

LI | 127 |

LII | 129 |

LIII | 131 |

LIV | 135 |

LXIII | 162 |

LXIV | 166 |

LXV | 167 |

LXVI | 168 |

LXVII | 170 |

LXVIII | 172 |

LXIX | 173 |

LXX | 175 |

LXXI | 180 |

LXXII | 182 |

LXXIII | 186 |

LXXIV | 190 |

LXXV | 193 |

LXXVI | 194 |

LXXVII | 197 |

LXXVIII | 199 |

LXXIX | 203 |

LXXX | 207 |

LXXXI | 208 |

LXXXII | 213 |

LXXXIII | 216 |

LXXXIV | 218 |

LXXXV | 224 |

LXXXVII | 226 |

LXXXVIII | 230 |

LXXXIX | 233 |

XC | 236 |

XCI | 238 |

XCII | 242 |

XCIII | 246 |

XCIV | 248 |

XCV | 250 |

XCVI | 252 |

XCVII | 253 |

XCVIII | 255 |

XCIX | 260 |

C | 267 |

301 | |

### Other editions - View all

Nonlinear Differential Equations and Dynamical Systems: With 107 Figures Ferdinand Verhulst No preview available - 1989 |

### Common terms and phrases

apply approximation asymptotically stable autonomous equation averaging behaviour bifurcation bounded called centre manifold chapter characteristic exponents closed orbit coefficients Consider equation Consider the equation Consider the system constant n x n-matrix contains convergent corresponding critical point degrees of freedom determined differential equations dimension domain dynamical system eigenvalues energy manifold equilibrium solution example expansion Figure fixed point flow follows Hamiltonian systems harmonic oscillator homoclinic orbit infinite number initial value problem instance integral invariant tori lemma linearisation Lipschitz-continuous Lyapunov exponents neighbourhood normal form normal mode normalisation obtain periodic points periodic solution perturbation phase phase-flow phase-plane phase-space plane Poincare Poincare-Bendixson theorem Poincare-mapping Pol-equation positive attractor positive constant produces quadratic resonance manifold result righthand side saddle point solution of equation Suppose system x T-periodic theory time-scale 1/e transformation transversal trivial solution unstable manifold variable vector function Verhulst Volterra-Lotka equations yields zero