{"product_id":"nonlinear-dynamics-and-chaos-isbn-9780471876847","title":"Nonlinear Dynamics and Chaos","description":"\u003cp\u003eNonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eExpands on the bestselling, highly regarded first edition\u003c\/li\u003e \u003cli\u003eA new chapter which will cover the new research in the area since first edition\u003c\/li\u003e \u003cli\u003eGlossary of terms and a bibliography have been added\u003c\/li\u003e \u003cli\u003eAll figures and illustrations will be 'modernised'\u003c\/li\u003e \u003cli\u003eComprehensive and systematic account of nonlinear dynamics and chaos, still a fast-growing area of applied mathematics\u003c\/li\u003e \u003cli\u003eHighly illustrated\u003c\/li\u003e \u003cli\u003eExcellent introductory text, can be used for an advanced undergraduate\/graduate course text\u003c\/li\u003e \u003c\/ul\u003eEin angesehener Bestseller - jetzt in der 2.aktualisierten Auflage! In diesem Buch finden Sie die aktuellsten Forschungsergebnisse auf dem Gebiet nichtlinearer Dynamik und Chaos, einem der am schnellsten wachsenden Teilgebiete der Mathematik. Die seit der ersten Auflage hinzugekommenen Erkenntnisse sind in einem zusätzlichen Kapitel übersichtlich zusammengefasst. \u003cp\u003ePreface vi\u003c\/p\u003e \u003cp\u003ePreface to the First Edition xv\u003c\/p\u003e \u003cp\u003eAcknowledgements from the First Edition xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Historical background 1\u003c\/p\u003e \u003cp\u003e1.2 Chaotic dynamics in Duffing's oscillator 3\u003c\/p\u003e \u003cp\u003e1.3 Attractors and bifurcations 8\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Basic Concepts of Nonlinear Dynamics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 An overview of nonlinear phenomena 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Undamped, unforced linear oscillator 15\u003c\/p\u003e \u003cp\u003e2.2 Undamped, unforced nonlinear oscillator 17\u003c\/p\u003e \u003cp\u003e2.3 Damped, unforced linear oscillator 18\u003c\/p\u003e \u003cp\u003e2.4 Damped, unforced nonlinear oscillator 20\u003c\/p\u003e \u003cp\u003e2.5 Forced linear oscillator 21\u003c\/p\u003e \u003cp\u003e2.6 Forced nonlinear oscillator: periodic attractors 22\u003c\/p\u003e \u003cp\u003e2.7 Forced nonlinear oscillator: chaotic attractor 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Point attractors in autonomous systems 26\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The linear oscillator 26\u003c\/p\u003e \u003cp\u003e3.2 Nonlinear pendulum oscillations 34\u003c\/p\u003e \u003cp\u003e3.3 Evolving ecological systems 41\u003c\/p\u003e \u003cp\u003e3.4 Competing point attractors 45\u003c\/p\u003e \u003cp\u003e3.5 Attractors of a spinning satellite 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Limit cycles in autonomous systems 50\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The single attractor 50\u003c\/p\u003e \u003cp\u003e4.2 Limit cycle in a neural system 51\u003c\/p\u003e \u003cp\u003e4.3 Bifurcations of a chemical oscillator 55\u003c\/p\u003e \u003cp\u003e4.4 Multiple limit cycles in aeroelastic galloping 58\u003c\/p\u003e \u003cp\u003e4.5 Topology of two-dimensional phase space 61\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Periodic attractors in driven oscillators 62\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Poincare map 62\u003c\/p\u003e \u003cp\u003e5.2 Linear resonance 64\u003c\/p\u003e \u003cp\u003e5.3 Nonlinear resonance 66\u003c\/p\u003e \u003cp\u003e5.4 The smoothed variational equation 71\u003c\/p\u003e \u003cp\u003e5.5 Variational equation for subharmonics 72\u003c\/p\u003e \u003cp\u003e5.6 Basins ofattraction by mapping techniques 73\u003c\/p\u003e \u003cp\u003e5.7 Resonance ofa self-exciting system 76\u003c\/p\u003e \u003cp\u003e5.8 The ABC ofnonlinear dynamics 79\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Chaotic attractors in forced oscillators 80\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Relaxation oscillations and heartbeat 80\u003c\/p\u003e \u003cp\u003e6.2 The Birkhoff±Shaw chaotic attractor 82\u003c\/p\u003e \u003cp\u003e6.3 Systems with nonlinear restoring force 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Stability and bifurcations of equilibria and cycles 106\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Liapunov stability and structural stability 106\u003c\/p\u003e \u003cp\u003e7.2 Centre manifold theorem 109\u003c\/p\u003e \u003cp\u003e7.3 Local bifurcations of equilibrium paths 111\u003c\/p\u003e \u003cp\u003e7.4 Local bifurcations of cycles 123\u003c\/p\u003e \u003cp\u003e7.5 Basin changes at local bifurcations 126\u003c\/p\u003e \u003cp\u003e7.6 Prediction ofincipient instability 128\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Iterated Maps as Dynamical Systems\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Stability and bifurcation of maps 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 135\u003c\/p\u003e \u003cp\u003e8.2 Stability of one-dimensional maps 138\u003c\/p\u003e \u003cp\u003e8.3 Bifurcations of one-dimensional maps 139\u003c\/p\u003e \u003cp\u003e8.4 Stability of two-dimensional maps 149\u003c\/p\u003e \u003cp\u003e8.5 Bifurcations of two-dimensional maps 156\u003c\/p\u003e \u003cp\u003e8.6 Basin changes at local bifurcations of limit cycles 158\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Chaotic behaviour of one- and two-dimensional maps 161\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 General outline 161\u003c\/p\u003e \u003cp\u003e9.2 Theory for one-dimensional maps 164\u003c\/p\u003e \u003cp\u003e9.3 Bifurcations to chaos 167\u003c\/p\u003e \u003cp\u003e9.4 Bifurcation diagram of one-dimensional maps 170\u003c\/p\u003e \u003cp\u003e9.5 He non map 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Flows, Outstructures, and Chaos\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 The geometry of recurrence 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Finite-dimensional dynamical systems 183\u003c\/p\u003e \u003cp\u003e10.2 Types ofrecurrent behaviour 187\u003c\/p\u003e \u003cp\u003e10.3 Hyperbolic stability types for equilibria 195\u003c\/p\u003e \u003cp\u003e10.4 Hyperbolic stability types for limit cycles 200\u003c\/p\u003e \u003cp\u003e10.5 Implications ofhyperbolic structure 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 The Lorenz system 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 A model ofthermal convection 207\u003c\/p\u003e \u003cp\u003e11.2 First convective instability 209\u003c\/p\u003e \u003cp\u003e11.3 The chaotic attractor ofLorenz 214\u003c\/p\u003e \u003cp\u003e11.4 Geometry ofa transition to chaos 222\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 2 RoÈssler's band 229\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 The simply folded band in an autonomous system 229\u003c\/p\u003e \u003cp\u003e12.2 Return map and bifurcations 233\u003c\/p\u003e \u003cp\u003e12.3 Smale's horseshoe map 238\u003c\/p\u003e \u003cp\u003e12.4 Transverse homoclinic trajectories 243\u003c\/p\u003e \u003cp\u003e12.5 Spatial chaos and localized buckling 246\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Geometry of bifurcations 249\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Local bifurcations 249\u003c\/p\u003e \u003cp\u003e13.2 Global bifurcations in the phase plane 258\u003c\/p\u003e \u003cp\u003e13.3 Bifurcations of chaotic attractors 266\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Applications in the Physical Sciences\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Subharmonic resonances of an offshore structure 285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Basic equation and non-dimensional form 286\u003c\/p\u003e \u003cp\u003e14.2 Analytical solution for each domain 288\u003c\/p\u003e \u003cp\u003e14.3 Digital computer program 289\u003c\/p\u003e \u003cp\u003e14.4 Resonance response curves 290\u003c\/p\u003e \u003cp\u003e14.5 Effect of damping 294\u003c\/p\u003e \u003cp\u003e14.6 Computed phase projections 296\u003c\/p\u003e \u003cp\u003e14.7 Multiple solutions and domains ofattraction 298\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Chaotic motions of an impacting system 302\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Resonance response curve 302\u003c\/p\u003e \u003cp\u003e15.2 Application to moored vessels 306\u003c\/p\u003e \u003cp\u003e15.3 Period-doubling and chaotic solutions 306\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Escape from a potential well 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 313\u003c\/p\u003e \u003cp\u003e16.2 Analytical formulation 314\u003c\/p\u003e \u003cp\u003e16.3 Overview ofthe steady-state response 319\u003c\/p\u003e \u003cp\u003e16.4 The two-band chaotic attractor 324\u003c\/p\u003e \u003cp\u003e16.5 Resonance ofthe steady states 328\u003c\/p\u003e \u003cp\u003e16.6 Transients and basins ofattraction 333\u003c\/p\u003e \u003cp\u003e16.7 Homoclinic phenomena 340\u003c\/p\u003e \u003cp\u003e16.8 Heteroclinic phenomena 346\u003c\/p\u003e \u003cp\u003e16.9 Indeterminate bifurcations 352\u003c\/p\u003e \u003cp\u003eAppendix 359\u003c\/p\u003e \u003cp\u003eIllustrated Glossary 369\u003c\/p\u003e \u003cp\u003eBibliography 402\u003c\/p\u003e \u003cp\u003eOnline Resources 428\u003c\/p\u003e \u003cp\u003eIndex 429\u003c\/p\u003e \u003cp\u003e\"... much more extensive than before.\" (\u003ci\u003eThe Mathematical Review\u003c\/i\u003e, March 2004)\u003c\/p\u003e \u003cp\u003e\"The fully updated second edition provides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos.\" (\u003ci\u003eInternational Journal of Environmental Analytical Chemistry\u003c\/i\u003e, Vol.84, No.14 – 15, 10 – 20 December 2004)\u003c\/p\u003e \u003cp\u003e\u003cb\u003eJohn Michael Tutill Thompson\u003c\/b\u003e, born on 7 June 1937 in Cottingham, England, is an Honorary Fellow in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. He is married with two children.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eH. B. Stewart\u003c\/b\u003e is the author of \u003ci\u003eNonlinear Dynamics and Chaos\u003c\/i\u003e, 2nd Edition, published by Wiley.\u003c\/p\u003e \u003cp\u003eCovering one of the fastest growing areas of applied mathematics, \u003ci\u003eNonlinear Dynamics and Chaos: Second Edition\u003c\/i\u003e, is a fully updated edition of this highly respected text. Covering a breadth of topics, ranging from the basic concepts to applications in the physical sciences, the book is highly illustrated and written in a clear and comprehensible style.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eProvides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos.\u003c\/li\u003e \u003cli\u003eIntroduces the concepts of instabilities, bifurcations, and catastrophes.\u003c\/li\u003e \u003cli\u003eEach idea is carefully explained and supported by examples.\u003c\/li\u003e \u003cli\u003eFeatures many applications to a wide variety of scientific fields.\u003c\/li\u003e \u003cli\u003eIncludes an illustrated glossary of geometrical dynamics.\u003c\/li\u003e \u003cli\u003eFeatures a supplementary bibliography of further reading.\u003c\/li\u003e \u003cli\u003eAssumes minimal background knowledge.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eNonlinear Dynamics and Chaos: Second Edition\u003c\/i\u003e provides an excellent introduction to the subject for students of mathematics, engineering, physics and applied science. It will also appeal to the many researchers who work with computer models of systems that change over time.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989695250661,"sku":"NP9780471876847","price":120.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471876847.jpg?v=1761785137","url":"https:\/\/k12savings.com\/es\/products\/nonlinear-dynamics-and-chaos-isbn-9780471876847","provider":"K12savings","version":"1.0","type":"link"}