Nonlinear dynamics and chaos. With applications to physics, biology, chemistry, and engineering. 2nd edition.

*(English)*Zbl 1343.37001
Boulder, CO: Westview Press (ISBN 978-0-8133-4910-7/pbk; 978-0-8133-4911-4/ebook). xiii, 513 p. (2015).

Publisher’s description: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.

A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.

##### MSC:

37-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

37N05 | Dynamical systems in classical and celestial mechanics |

37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |

37N25 | Dynamical systems in biology |