Chaos: concepts, control and constructive use. 2nd edition. (English) Zbl 1349.37001
Understanding Complex Systems; Springer: Complexity. Cham: Springer (ISBN 978-3-319-42495-8/hbk; 978-3-319-42496-5/ebook). xi, 281 p. (2017).
Publisher’s description: This book offers a short and concise introduction to the many facets of chaos theory.
While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example.
The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others.
The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others.
This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently.
See the review of the first edition in [Zbl 1178.37001].
While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example.
The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others.
The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others.
This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently.
See the review of the first edition in [Zbl 1178.37001].
MSC:
37-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory |
82-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics |
81-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory |
37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
81Q50 | Quantum chaos |
70K50 | Bifurcations and instability for nonlinear problems in mechanics |
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |