Chaos occurs widely in engineering and natural systems. Historically it has been noted only as irregular or unpredictable behaviour and often attributed to random external influences. Further studies have shown that chaotic phenomena are completely deterministic and characteristic for typical nonlinear systems. These studies posed the question of the practical applications of chaos. One of the possible answers is to control chaotic behaviour in such a way as to make it predictable. Recently there have been examples of the potential usefulness of chaotic behaviour and this has caused growing interest among engineers and applied scientists. In this book the new mathematical ideas in nonlinear dynamics are described such that engineers can apply them in real physical systems.
Auflage
Softcover reprint of the original 1st ed. 1998
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Produkt-Hinweis
Illustrationen
2 s/w Tabellen
black & white illustrations
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Dicke: 8 mm
Gewicht
ISBN-13
978-3-540-63515-4 (9783540635154)
DOI
10.1007/978-3-642-97719-0
Schweitzer Klassifikation
1. Response of a Nonlinear System.- Problems.- 2. Continuous Dynamical Systems.- 2.1 Phase Space and Attractors.- 2.2 Fixed Points and Linearisation.- 2.3 Relation Between Nonlinear and Linear Systems.- 2.4 Poincaré Map.- 2.5 Lyapunov Exponents and Chaos.- 2.6 Spectral Analysis.- 2.7 Description of Different Attractors.- 2.8 Reconstruction of Attractor from Time Series.- Problems.- 3. Discrete Dynamical Systems.- 3.1 Introductory Example.- 3.2 One-Dimensional Maps.- 3.3 Bifurcations of One-Dimensional Maps.- 3.4 One-Dimensional Maps and Higher-Dimensional Systems.- Problems.- 4. Fractals.- 4.1 The Cantor Set.- 4.2 Fractal Dimensions.- 4.3 Fractal Sets.- 4.4 Smale Horseshoe.- 4.5 Fractal Basin Boundaries.- Problems.- 5. Routes to Chaos.- 5.1 Period Doubling.- 5.2 Quasiperiodic Route.- 5.3 Intermittency.- 5.4 Duffing's Equation: Discrete Dynamics Approach.- 5.5 Condition for Chaos by Period-Doubling Route.- Problems.- 6. Applications.- 6.1 Chaos in Systems with Dry Friction.- 6.2 Chaos in Chemical Reactions.- 6.3 Elastica and Spatial Chaos.- 6.4 Electronic Circuits and Chaos.- 6.5 Chaos in El Nino Events Model.- 7. Controlling Chaos.- 7.1 Controlling Methods.- 7.1.1 Control Through Feedback.- 7.1.2 Control by System Design.- 7.1.3 Selection of Controlling Method.- 7.2 Synchronization of Chaos.- 7.2.1 Pecora and Carroll's Approach.- 7.2.2 Synchronization by Continuous Control.- 7.3 Secure Communication.- References.
