introduction to applied nonlinear dynamical systems and chaos pdf

Introduction To Applied Nonlinear Dynamical Systems And Chaos Pdf

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AMATH 502 A: Introduction to Dynamical Systems and Chaos

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. In the 20 years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics.

Necessary and sufficient conditions on the existence and stability of the fixed points of this system are established. By applying the center manifold theorem and bifurcation theory, we show that the system has the fold bifurcation, flip bifurcation, and Neimark-Sacker bifurcation under certain conditions. Numerical simulations are presented to not only show the consistence between examples and our theoretical analysis, but also exhibit complexity and interesting dynamical behaviors, including period, , , , , , and orbits, quasi-periodic orbits, chaotic behaviors which appear and disappear suddenly, coexisting chaotic attractors. Chen , The function cascade synchronization scheme for discrete-time hyperchaotic systems, Commun Nonlinear Sci Numer Simulat , 14 , Google Scholar.

Wiggins S. Springer, This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research.

Introduction to applied nonlinear dynamical systems and chaos

This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as students of mathematics. This new edition contains extensive new material on invariant manifold theory and normal forms in particular, Hamiltonian normal forms and the role of symmetry. Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. It does not only contain much new material, for instance on invariant manifold theory and normal forms, it has also been restructured.


Introduction to applied nonlinear dynamical systems and chaos / Stephen Wiggins. — 2nd ed. p. cm. — (Texts in applied mathematics ; 2).


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About this book

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Скорее. ГЛАВА 44 Фил Чатрукьян, киля от злости, вернулся в лабораторию систем безопасности. Слова Стратмора эхом отдавались в его голове: Уходите немедленно. Это приказ. Чатрукьян пнул ногой урну и выругался вслух - благо лаборатория была пуста: - Диагностика, черт ее дери.

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