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- catalog abstract "As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustrates how the methods can be used in a variety of applications. The first half of the book concentrates on finding approximations to random processes using the methodologies of probability theory. The second half of the book derives approximations to solutions of various problems in mechanics, electronic circuits, population biology, and genetics. In each example, the underlying physical or biological phenomenon is described in terms of nonrandom models taken from the literature, and the impact of random noise on the solutions is investigated. The mathematical problems in these applicitons involve random pertubations of gradient systems, Hamiltonian systems, toroidal flows, Markov chains, difference equations, filters, and nonlinear renewal equations. The models are analyzed using the approximation methods described here and are visualized using MATLAB-based computer simulations. This book will appeal to those researchers and graduate students in science and engineering who require tools to investigate stochastic systems.".
- catalog contributor b12633739.
- catalog contributor b12633740.
- catalog contributor b12633741.
- catalog contributor b12633742.
- catalog created "c2002.".
- catalog date "2002".
- catalog date "c2002.".
- catalog dateCopyrighted "c2002.".
- catalog description "As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustrates how the methods can be used in a variety of applications. The first half of the book concentrates on finding approximations to random processes using the methodologies of probability theory. The second half of the book derives approximations to solutions of various problems in mechanics, electronic circuits, population biology, and genetics. In each example, the underlying physical or biological phenomenon is described in terms of nonrandom models taken from the literature, and the impact of random noise on the solutions is investigated. The mathematical problems in these applicitons involve random pertubations of gradient systems, Hamiltonian systems, toroidal flows, Markov chains, difference equations, filters, and nonlinear renewal equations. The models are analyzed using the approximation methods described here and are visualized using MATLAB-based computer simulations. This book will appeal to those researchers and graduate students in science and engineering who require tools to investigate stochastic systems.".
- catalog description "Includes bibliographical references (p. [472]-484) and index.".
- catalog description "Introduction -- Ergodic Theorems -- Convergence Properties of Stochastic Processes -- Averaging -- Normal Deviation -- Diffusion Approximation -- Stability -- Markov Chains with Random Transition Probabilities -- Randomly Perturbed Mechanical Systems -- Dynamical Systems on a Torus -- The Phase Locked Loop -- Models in Population Biology -- Genetics -- Appendices -- Index.".
- catalog extent "xi, 488 p. :".
- catalog identifier "0387954279 (acid-free paper)".
- catalog isPartOf "Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 150.".
- catalog isPartOf "Applied mathematical sciences ; 150".
- catalog issued "2002".
- catalog issued "c2002.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "510 s 515/.35 21".
- catalog subject "Differentiable dynamical systems.".
- catalog subject "Distribution (Probability theory).".
- catalog subject "Mathematical physics.".
- catalog subject "Mathematics.".
- catalog subject "Mechanics, applied.".
- catalog subject "Perturbation (Mathematics)".
- catalog subject "QA1 .A647 vol. 150b QA871".
- catalog tableOfContents "Introduction -- Ergodic Theorems -- Convergence Properties of Stochastic Processes -- Averaging -- Normal Deviation -- Diffusion Approximation -- Stability -- Markov Chains with Random Transition Probabilities -- Randomly Perturbed Mechanical Systems -- Dynamical Systems on a Torus -- The Phase Locked Loop -- Models in Population Biology -- Genetics -- Appendices -- Index.".
- catalog title "Random perturbation methods with applications in science and engineering / Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi.".
- catalog type "text".