## Differential Equations, Bifurcations, and Chaos in EconomicsAlthough the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics. |

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### Contents

Differential Equations in Economics | 1 |

Scalar Linear Differential Equations | 16 |

Scalar Nonlinear Differential Equations | 53 |

Economic Dynamics with Scalar Differential Equations | 92 |

Planar Linear Differential Equations | 156 |

Planar Nonlinear Differential Equations | 182 |

Planar Dynamical Economical Systems | 241 |

HigherDimensional Differential Equations | 304 |

HigherDimensional Nonlinear Differential Equations | 329 |

HigherDimensional Economic Evolution | 382 |

Economic Evolution with Changeable Speeds and Structures | 446 |

Appendix | 455 |

475 | |

483 | |

### Common terms and phrases

applied assume asymptotically stable behavior bifurcation theorem budget constraint capital stocks center manifold center manifold theorem coefficients constant consumers consumption corresponding critical point curve defined denote derivatives determined dimensional dynamic system economic system eigenvalues eigenvectors equation yields equilibrium point examine Example Consider existence first-order given growth model growth rate Hence homogeneous Hopf bifurcation Hopf bifurcation theorem human capital increases initial conditions introduce investment Jacobian labor Lemma Liapunov function Lienard system limit cycle linear differential equation linear system linearly independent Lorenz Lorenz equations neighborhood nonlinear system orbit origin output parameter periodic solution planar linear population positive definite problem production function propensity rate of interest region respectively satisfies Section sector solve specified structure Substituting Eqs system x theory trajectory unique equilibrium unique solution unstable utility function variables vector field wage rate wealth zero Zhang

### References to this book

Monetary Growth Theory: Money, Interest, Prices, Capital, Knowledge and ... Wei-Bin Zhang No preview available - 2008 |