## Introduction to Chaos and CoherenceIntroduction to Chaos and Coherence provides a clear introduction to the theory of chaotic systems, with a minimum of mathematical complexity. Used extensively in this color-illustrated book, Lyapunov exponents are convenient tools for exploring models of chaotic systems. Aimed primarily at advanced undergraduate students of physics and applied math, the book will also be of value to anyone with an interest in a mathematical approach to their subject, in particular, chemists, astronomers, and life and earth scientists. |

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### Contents

The logistic map CD | 9 |

Higher dimensional maps | 49 |

Conservative maps | 80 |

The Lorenz model | 101 |

Appendices | 119 |

Further Reading | 126 |

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### Common terms and phrases

Arnol’d tongues basin of attraction Cantor set cellular automata chaotic orbit chaotic region circle map coefﬁcients complex conjugated components conservative maps consider constant corresponding COUPLED LOGISTIC MAP critical point curves deﬁned deﬁnition dynamical systems eigenvalues eigenvectors elliptic points exponential Figure ﬁnd ﬁnite number ﬁrst ﬂows fractal dimension function given gives Hénon map heteroclinic higher dimensional maps homoclinic orbit Hopf bifurcation in-phase inﬁnitesimal inﬁnity initial conditions interval iterate Jacobian matrix length linear logistic map Lorenz model Lyapunov exponent means motion negative nonlinear one-dimensional origin oscillations out-of-phase parameter point parameter space period doubling bifurcation period one orbit period three orbit period two orbit phase space plate plot possible pre-images quasiperiodic Reproduced with permission result reversed bifurcation sequence shown in ﬁgure solutions stable and unstable stable ﬁxed point stochastic term strange attractor sufﬁciently superstable tangent bifurcation TWO-DIMENSIONAL COUPLED LOGISTIC unstable manifold variable vector winding number zero