Leseprobe
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Chaos and Dynamical Systems
David P. Feldman
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Parameter, Counterexample, Deterministic system, Dimension, Phase plane, Predictive modelling, Catastrophe theory, Initial value problem, Counterintuitive, Phase line (mathematics), Diagram (category theory), State diagram, Instability, Critical exponent, Stochastic, Lorenz system, Two-dimensional space, Bifurcation diagram, Emergence, Quantum fluctuation, Limit cycle, Bifurcation theory, Equations of motion, Existential quantification, Reductionism, Phase transition, Thermodynamic system, Prediction, Fractal dimension, Weighted arithmetic mean, Logistic map, Variable (mathematics), Critical phenomena, Dynamical system, Mathematics, Equation, Antiderivative, Oscillation, Transcritical bifurcation, Random sequence, Iteration, Renormalization group, Complex adaptive system, Arbitrariness, Nonlinear system, Order and disorder (physics), Time series, Chaos theory, Statistical fluctuations, Power rule, Logistic function, Differential equation, Power law, Symbolic dynamics, Extrapolation, Phase space, Renormalization, Mathematical problem, Reynolds number, Differentiable manifold, Mean field theory, Lyapunov exponent, Attractor, Derivative, Initial condition, Iterated function, Autocorrelation, Stochastic process, Irreversible process, Euler method