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 the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics.

Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry And Engineering (Studies in Nonlinearity)

Science & Math

Strogatz, Steven H.

Mathematics

CRC-Press

The goal of this Third Edition is the same as previous editions: to provide a good foundation - and a joyful experience! - for anyone who'd like to learn about nonlinear dynamics and chaos from an applied perspective. 
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, strange attractors, and synchronization. 
The prerequisites are comfort with multivariable calculus and linear algebra, as well as a first course in physics. 
Changes to this edition include substantial exercises about conceptual models of climate change, an updated treatment of the SIR model of epidemics, and amendments (based on recent research) about the Selkov model of oscillatory glycolysis. Equations, diagrams, and explanations have been reconsidered and often revised. There are also about 50 new references, many from the recent literature. 
The most notable change is a new chapter about the Kuramoto model. 
This icon of nonlinear dynamics, introduced in 1975 by the Japanese physicist Yoshiki Kuramoto, is one of the rare examples of a high-dimensional nonlinear system that can be solved by elementary means. It provides an entrée to current research on complex systems, synchronization, and networks, yet is accessible to newcomers. 
Students and teachers have embraced the book in the past for its exceptional clarity and rich applications, and its general approach and framework continue to be sound.

Nonlinear Dynamics and Chaos

Chapman and Hall/CRC

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.

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering

Nonlinear Dynamics and Chaos, With Applications to Physics, Biology, Chemistry and Engineering

The Joy Of X: A Guided Tour of Math, from One to Infinity

Mariner Books

"Sync" is the story of a dazzling kind of order in the universe, the harmony that comes from cycles in sync. The tendency to synchronize is one of the most far-reaching drives in all of nature. It extends from people to planets and from animals to atoms. Steve Strogatz looks at human sleep rhythms, menstrual synchrony, insect swarms, superconductors, lasers, heart rhythms and codes, showing how self-organization produces our coherent world.

Sync : The Emerging Science of Spontaneous Order

Allen Lane.

Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity)

Chemistry

At the heart of the universe is a steady, insistent beat, the sound of cycles in sync. Along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison; the moon spins in perfect resonance with its orbit around the earth; our hearts depend on the synchronous firing of ten thousand pacemaker cells. While the forces that synchronize the flashing of fireflies may seem to have nothing to do with our heart cells, there is in fact a deep connection. Synchrony is a science in its infancy, and Strogatz is a pioneer in this new frontier in which mathematicians and physicists attempt to pinpoint just how spontaneous order emerges from chaos. From underground caves in Texas where a French scientist spent six months alone tracking his sleep-wake cycle, to the home of a Dutch physicist who in 1665 discovered two of his pendulum clocks swinging in perfect time, this fascinating book spans disciplines, continents, and centuries. Engagingly written for readers of books such as Chaos and The Elegant Universe, Sync is a tour-de-force of nonfiction writing.

Sync: The Emerging Science of Spontaneous Order

Computers & Technology

Computer Science

Grand Central Publishing

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 twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting fields as systems biology, evolutionary game theory, and socio-physics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as curiosities of visual perception and the tumultuous love dynamics in Gone with the Wind.

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition (Studies in Nonlinearity)

Westview Press

Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition (Studies in Nonlinearity)

Biological Sciences

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