## Mathematics for Dynamic ModelingThis new edition of Mathematics for Dynamic Modeling updates a widely used and highly-respected textbook. The text is appropriate for upper-level undergraduate and graduate level courses in modeling, dynamical systems, differential equations, and linear multivariable systems offered in a variety of departments including mathematics, engineering, computer science, and economics. The text features many different realistic applications from a wide variety of disciplines.The book covers important tools such as linearization, feedback concepts, the use of Liapunov functions, and optimal control. This new edition is a valuable tool for understanding and teaching a rapidly growing field. Practitioners and researchers may also find this book of interest. * Contains a new chapter on stability of dynamic models * Covers many realistic applications from a wide variety of fields in an accessible manner * Provides a broad introduction to the full scope of dynamical systems * Incorporates new developments such as new models for chemical reactions and autocatalysis * Integrates MATLAB throughout the text in both examples and illustrations * Includes a new introduction to nonlinear differential equations |

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### Contents

Simple Dynamic Models | 3 |

Ordinary Differential Equations | 15 |

Stability of Dynamic Models | 29 |

There Is a Better | 55 |

A Summary of Part 1 | 71 |

Cycles and Bifurcation | 121 |

treatment no proof of Thorns theorem on fold and cusp | 153 |

Bifurcation and Catastrophe | 170 |

Chaos | 185 |

References and a Guide to Further Readings | 207 |

### Common terms and phrases

assume attractor axis basin of attraction behavior budworm cars catastrophe model Chapter closed orbit Consider corresponding curve cusp catastrophe decreases defined denote density depends diastole differential equation discussion dynamical systems eigenvalues Example Exercise fiber fold catastrophe follows frictional given gives gradient systems growth Hopf bifurcation horizontal increases initial intersection Jacobian matrix jumps Liapunov function limit cycle limit cycle exists linearized system mass mass-spring system mathematical maximum motion moves negative nullcline obtain occurs optimal orbit that begins oscillator parameters pendulum phase plane pitchfork bifurcation plankton Pol equation pollutant population predator proportional rest point restoring force rocket roots rotates saddle point satisfies scalar Section shown in Figure shows slope smooth smoothly deformable spatial stable equilibrium stable manifold stimulus Suppose systole tangent tension Theorem traffic traveling wave solution unstable variable vary vector field velocity vertical zero

### Popular passages

Page 216 - How Random is a Coin Toss?", Physics Today, April 1983, 1-8, and L. Kadanoff, "Roads to Chaos,