Articles liés à Nonlinear Dynamics and Chaos: Where Do We Go from Here?
Synopsis
Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such systems? Written by international experts, Nonlinear Dynamics and Chaos: Where Do We Go from Here? assesses what the future holds for dynamics and chaos. The chapters address one or more of the broad and interconnected main themes: neural and biological systems, spatially extended systems, and experimentation in the physical sciences. The contributors offer suggestions as to what they see as the way forward, often in the form of open questions for future research.
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À propos de l?auteur
J Hogan, A.R Krauskopf, Mario di Bernado, Eddie R. Wilson, Hinke M. Osinga, Martin E. Homer, Alan R. Champneys
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Nonlinear Dynamics and Chaos: Where Do We Go from Here?
Edité par
IoP Institute of Physics Publishing, 2003
ISBN 10 : 0750308621
ISBN 13 : 9780750308625
Ancien ou d'occasion
Couverture rigide
Edition originale
Vendeur : killarneybooks, Inagh, CLARE, Irlande
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Hardcover. Etat : Good. 1st Edition. Hardcover, xi + 358 pages, NOT ex-library. Good condition, clean with unmarked text, no inscriptions, no stamps. Issued without a dust jacket. -- The book brings together 13 chapters, combining state-of-the-field reviews with forward-looking research agendas. The unifying premise is the recognition that while nonlinear dynamics has achieved significant theoretical and computational development, particularly in low-dimensional systems, its future depends on extending methodologies to high-dimensional, spatiotemporal, stochastic, and biologically grounded contexts. The chapters are organized around three interconnected themes: neural and biological systems, spatially extended systems, and experimentation in the physical sciences. Chapter 1 explores bifurcation theory in systems with multiple time scales, emphasizing degenerate decomposition in contexts such as neuronal models. It shows how traditional analytical tools struggle with singular perturbations and calls for refined geometric and computational techniques. Chapter 2 transitions to quantum many-body systems, focusing on nonlinear manifestations such as quantum discrete breathers, and poses mathematical challenges in reconciling nonlinearity with quantum superposition principles. Chapter 3 examines hereditary systems and difference-differential equations, extending bifurcation analysis to systems incorporating memory and delay. The following section discusses stabilizing structures in nonlinear optics, including the creation of stable pulses from interacting unstable waves, and addresses global vs local nonlinear behaviors. Chapter 5 analyzes spatiotemporal communication through chaotic optical signals, linking nonlinear laser dynamics with synchronization theory. Chapter 6 outlines outstanding challenges in pattern formation theory, particularly in lattice systems, nearly inviscid flows, and systems with broken symmetry. It emphasizes limitations of weakly nonlinear approaches in predicting fully nonlinear outcomes. In Chapter 7, Mullin critiques the relevance of chaos theory in fluid mechanics, using Taylor-Couette flow as a central case. He interrogates the extent to which low-dimensional chaotic models capture fluid behavior and identifies the need for experimental frameworks better suited to spatiotemporal complexity. Chapter 8 presents time-reversal acoustics, showing how chaotic cavity dynamics can be exploited for wave focusing, with implications for medical imaging and seismology. Kuramoto's Chapter 9 turns to non-locally coupled oscillators, developing reduction methods for systems between the locally and globally coupled extremes. He introduces new classes of dynamics such as rotating spiral waves without phase singularities. Chapter 10 investigates vortex dynamics in nonlinear media, proposing prime-number-based formulations to analyze organizing centers such as spiral wave filaments in excitable systems. Chapter 11 (Bressloff & Cowan) focuses on spontaneous pattern formation in the primary visual cortex, drawing from symmetry-based models like the Ginzburg-Landau and amplitude equations to describe orientation tuning and columnar structures. Chapter 12 (Ermentrout & Osan) models morphogenetic patterning during development, bridging computational neuroscience with biological morphogenesis using feature maps and competitive dynamics. The final chapter, by Ditto, emphasizes spatiotemporal dynamics as central to future nonlinear science, particularly in biomedical contexts like cardiac fibrillation and neurocomputing. Collectively, the volume addresses the limitations of traditional nonlinear dynamics in capturing real-world complexity, advocating for hybrid approaches combining mathematical rigor, computational scalability, and biological relevance. The book introduces tools from geometric singular perturbation, symmetry analysis, pattern theory, and dynamical systems reduction, while engaging with experimental domains ranging from neuroscience to optics. N° de réf. du vendeur 011449
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Nonlinear Dynamics and Chaos
Vendeur : PBShop.store US, Wood Dale, IL, Etats-Unis
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HRD. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur FT-9780750308625
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Nonlinear Dynamics and Chaos
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
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HRD. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur FT-9780750308625
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Nonlinear Dynamics and Chaos
Vendeur : moluna, Greven, Allemagne
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Gebunden. Etat : New. J Hogan, A.R Krauskopf, Mario di Bernado, Eddie R. Wilson, Hinke M. Osinga, Martin E. Homer, Alan R. ChampneysNonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on . N° de réf. du vendeur 898571033
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Nonlinear Dynamics and Chaos: Where do we go from here?
Edité par
Taylor & Francis Ltd, 2002
ISBN 10 : 0750308621
ISBN 13 : 9780750308625
Neuf
Couverture rigide
Vendeur : THE SAINT BOOKSTORE, Southport, Royaume-Uni
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Hardback. Etat : New. New copy - Usually dispatched within 4 working days. 806. N° de réf. du vendeur B9780750308625
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Nonlinear Dynamics and Chaos : Where Do We Go from Here?
Vendeur : GreatBookPrices, Columbia, MD, Etats-Unis
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Etat : New. N° de réf. du vendeur 745886-n
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Nonlinear Dynamics and Chaos : Where Do We Go from Here?
Vendeur : GreatBookPricesUK, Woodford Green, Royaume-Uni
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Etat : New. N° de réf. du vendeur 745886-n
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Nonlinear Dynamics and Chaos: Where do we go from here?
Edité par
Inst of Physics Pub Inc, 2002
ISBN 10 : 0750308621
ISBN 13 : 9780750308625
Neuf
Couverture rigide
Vendeur : Revaluation Books, Exeter, Royaume-Uni
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Hardcover. Etat : Brand New. 1st edition. 376 pages. 9.00x6.00x0.75 inches. In Stock. N° de réf. du vendeur __0750308621
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Nonlinear Dynamics and Chaos : Where Do We Go from Here?
Edité par
CRC Press, 2002
ISBN 10 : 0750308621
ISBN 13 : 9780750308625
Ancien ou d'occasion
Couverture rigide
Vendeur : GreatBookPrices, Columbia, MD, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Etat : As New. Unread book in perfect condition. N° de réf. du vendeur 745886
Quantité disponible : 1 disponible(s)
Image fournie par le vendeur
Nonlinear Dynamics and Chaos : Where Do We Go from Here?
Edité par
CRC Press, 2002
ISBN 10 : 0750308621
ISBN 13 : 9780750308625
Ancien ou d'occasion
Couverture rigide
Vendeur : GreatBookPricesUK, Woodford Green, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
Etat : As New. Unread book in perfect condition. N° de réf. du vendeur 745886
Quantité disponible : 1 disponible(s)