## Attractors, Bifurcations, & Chaos: Nonlinear Phenomena in EconomicsThe present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics chapters -on partial differential equations, and on bifurcations and catastrophe theory -thus making the mathematical background material fairly complete. The author is happy that this new book did rather well, but he preferred to rewrite it, rather than having just a new print run. Material, stemming from the first versions, was more than ten years old, while nonlinear dynamics has been a fast developing field, so some analyses looked rather old-fashioned and pedestrian. The necessary revision turned out to be rather substantial. |

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### Contents

1 | |

13 | |

Iterated Maps or Difference Equations | 161 |

Bifurcation and Catastrophe | 217 |

Monopoly | 239 |

Duopoly and Oligopoly | 261 |

Continuous Time | 307 |

Continuous Space | 357 |

Discrete Time | 381 |

Invariant Spaces | 430 |

Increasing Complexity | 471 |

Multiple Attractors | 503 |

528 | |

543 | |

### Other editions - View all

Attractors, Bifurcations, & Chaos: Nonlinear Phenomena in Economics Tönu Puu No preview available - 2010 |

Attractors, Bifurcations, and Chaos: Nonlinear Phenomena in Economics Tönu Puu No preview available - 2014 |

### Common terms and phrases

absorbing area Accordingly amplitude attraction basins basins of attraction becomes bifurcation diagram boundary conditions catastrophe chaos chaotic attractor circle coefficients coexistent complex consider constant convergence coordinates cosé Cournot point critical lines cubic defined denoted derivative determinant differential equations dimension dimensional display divergence dynamical system economics eigenvalues equilibrium fact finite fixed point fold fractal frequency function hence income infinity initial conditions integral intersection invariant curve invariant plane iteration Jacobian limit cycle linear linearised logistic logistic map loses stability Lyapunov exponent monkey saddle motion negative Neimark bifurcation node nonlinear nonzero obtain orbits origin oscillator pair parameter value period doubling phase space picture Poincaré section positive potential produce quasiperiodic region represents right hand side saddle points second order simulation sine singular sinix solution solve spatial square structurally stable Substituting theorem tion tongues torus trajectories unstable variables vector vertical wave whereas