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Chaos and Dynamical Systems

David Feldman

ca. 33,99
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik


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.

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Deterministic system, Laplace's demon, Stochastic calculus, Transcritical bifurcation, Initial condition, Arbitrarily large, Bifurcation theory, Leibniz's notation, Thermodynamic system, Power rule, Observational error, Autocorrelation, Chaos theory, Irreversible process, Mathematics, Theory of computation, Lyapunov exponent, Quantum fluctuation, Initial value problem, Renormalization, Counterintuitive, Instability, Quantity, Iterated function, Time series, Power law, Saddle-node bifurcation, Stochastic, Iteration, Limit cycle, Vibration, Prediction, Antiderivative, Deterministic system (philosophy), Derivative, Logistic function, Mean field theory, Differentiable manifold, Butterfly effect, Idealization, Nonlinear Dynamics (journal), F-distribution, Maxima and minima, Ordinary differential equation, Fractal dimension, Order and disorder (physics), Thermodynamic equilibrium, Nonlinear system, Logistic map, Phase space, Linear equation, Reductionism, Mathematical optimization, Schwarzian derivative, Fluid dynamics, Equation, Existential quantification, Extrapolation, Oscillation, Parameter, Stochastic process, Arbitrary unit, Predictive modelling, Lorenz system, Critical exponent, Catastrophe theory, Two-dimensional space, Phase transition, Dimension, Differential equation, Equations of motion, Renormalization group, Counterexample, Weighted arithmetic mean, Phase plane, Nondimensionalization, Bifurcation diagram, Diagram (category theory), State-space representation, Arbitrariness, Theory, Critical phenomena, Emergence, Euler method, Reynolds number, Symbolic dynamics, Universality class, Regime shift, Variable (mathematics), Partial differential equation, Statistical fluctuations, Complex adaptive system, Dynamical system, Mathematical problem, Phase line (mathematics), Negative number, State diagram, Attractor, Limit point, Random sequence