## Perspectives of Nonlinear Dynamics:The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book and its companion volume, Perspectives of nonlinear dynamics, volume 1, the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations. The text is complemented by copious references, extensive historical and bibliographical notes, exercises and examples, and appendices giving more details of some mathematical ideas. Each chapter includes an extensive section commentary on the exercises and their solution. Graduate students and research workers in physics, applied mathematics, chemistry, biology and engineering will welcome these volumes as the first broad introduction to this important major field of research. |

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### Contents

First order differential systems | 1 |

harmonic lattice in a periodic potential toroidal magnetic Fields twist maps | 33 |

Models based on third order differential systems | 125 |

Mobius band manifolds some interacting flows from neighboring saddle | 132 |

of r contracting and global attracting character | 138 |

discussion of possible relations the KaplanYorke conjecture | 217 |

prediction of the integrability of equalmass Toda lattices the Flaschka | 281 |

solitons and nonsolitons | 348 |

Coupled maps CM and cellular automata CA | 427 |

Understanding complex systems Order organization Endnotemodels | 505 |

Appendixes | 529 |

Bibliography | 553 |

621 | |

627 | |

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### Common terms and phrases

arbitrary area-preserving area-preserving map asymptotic basins of attraction behavior bifurcation cells cellular chaos chaotic Chapter closed curve coefficients complex configurations consider constant defined determine differential equations diffusion dimensions discussed Dynamical Systems energy entropy ergodic example Exercise figure finite fixed point flow function global Hence Henon homoclinic hyperbolic hyperbolic fixed points illustrated in Fig infinite number initial conditions integrable interaction invariant iterates Julia set KAM theorem KdV equation lattice limit cycle linear Lorenz Lorenz model Lyapunov exponents Math mathematical Moreover motion nonlinear Note obtain one-dimensional oscillator parameter particles partition periodic orbit periodic solutions perturbation phase space Phys plane Poincare map Poincare's properties region Rossler rotation number satisfies sequence set of points simple solitons spatial Springer-Verlag stable manifold standard map strange attractor structure theorem theory Toda lattice topological torus trajectories transformation two-dimensional unstable values variables velocity wave yields zero