Chaos and Dynamical Systems (eBook)

David P. Feldman (Autor)

eBook Download: PDF

2019
264 Seiten
Princeton University Press (Verlag)
978-0-691-18939-0 (ISBN)

Infos

Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview.In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.

Autor

David P. Feldman is professor of physics and mathematics at the College of the Atlantic. He is the author of Chaos and Fractals: An Elementary Introduction.

Produkt-Details

• Erscheint lt. Verlag: 6.8.2019
• Reihe/Serie: Primers in Complex Systems
• Reihe/Serie: Primers in Complex Systems
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Schlagworte: Antiderivative • Arbitrarily large • arbitrariness • Arbitrary unit • attractor • autocorrelation • Bifurcation diagram • Bifurcation Theory • Butterfly effect • Catastrophe Theory • chaos theory • complex adaptive system • counterexample • counterintuitive • critical exponent • Critical Phenomena • Derivative • Deterministic system • Deterministic system (philosophy) • Diagram (category theory) • differentiable manifold • differential equation • Dimension • Dynamical system • Emergence • Equation • Equations of motion • Euler Method • existential quantification • Extrapolation • F-distribution • Fluid Dynamics • fractal dimension • idealization • Initial Condition • Initial Value Problem • instability • Irreversible process • Iterated function • Iteration • Laplace's demon • Leibniz's notation • Limit cycle • Limit point • linear equation • logistic function • logistic map • Lorenz System • Lyapunov exponent • Mathematical Optimization • Mathematical problem • Mathematics • Maxima and minima • Mean field theory • Negative number • Nondimensionalization • Nonlinear Dynamics (journal) • nonlinear system • Observational error • Order and disorder (physics) • ordinary differential equation • Oscillation • Parameter • partial differential equation • Phase line (mathematics) • phase plane • Phase space • phase transition • power law • Power rule • Prediction • Predictive Modelling • Quantity • Quantum fluctuation • random sequence • reductionism • Regime shift • renormalization • Renormalization Group • Reynolds Number • Saddle-node bifurcation • Schwarzian derivative • State diagram • State-space Representation • statistical fluctuations • stochastic • Stochastic Calculus • Stochastic process • symbolic dynamics • theory • Theory of Computation • Thermodynamic Equilibrium • Thermodynamic system • Time Series • Transcritical bifurcation • two-dimensional space • Universality class • Variable (mathematics) • Vibration • Weighted arithmetic mean
• ISBN-10: 0-691-18939-0 / 0691189390
• ISBN-13: 978-0-691-18939-0 / 9780691189390