Analysis of the SDE/Monte Carlo Approach in Studying Nonlinear Systems

Rex J. Fleming

ISBN 10: 365971514X / ISBN 13: 9783659715143

Published by LAP LAMBERT Academic Publishing Jun 2015, 2015

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -The reader is about to embark on a tutorial journey through a series of nonlinear dynamic systems that contain a rich tapestry of phenomena and solutions. The study of nonlinear systems can be greatly enhanced by the combined use of the stochastic dynamic equations and Monte Carlo calculations. When a dynamic system is forced and dissipative all the trajectories tend toward a bounded set of zero volume - often a strange attractor with a fractal dimension. The stochastic dynamic equations can directly reveal the statistical moments of the system, but their direct solution is inefficient, and they are not a closed set. The power of the combined method is that the time averaged Monte Carlo moments will agree exactly with equations described by the left hand side of the full stochastic dynamic equations set to zero - no closure is required. Every equation expresses an exact relationship among the variables. One is able to delve far deeper into the nature of the nonlinear systems. This tutorial exposition offers the tools for the past nonlinear modeling efforts in the traditional physical sciences and in various complex modeling problems in new fields of biology and health sciences. 144 pp. Englisch.

Seller Inventory # 9783659715143

Bibliographic Details

• Title: Analysis of the SDE/Monte Carlo Approach in Studying Nonlinear Systems
• Publisher: LAP LAMBERT Academic Publishing Jun 2015
• Publication Date: 2015
• Language: English
• ISBN 10: 365971514X
• ISBN 13: 9783659715143
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 9D millimeters 220 millimeters width by 150 millimeters height by 9 millimeters depth
• Weight: 233 grams

About this title

Synopsis

The reader is about to embark on a tutorial journey through a series of nonlinear dynamic systems that contain a rich tapestry of phenomena and solutions. The study of nonlinear systems can be greatly enhanced by the combined use of the stochastic dynamic equations and Monte Carlo calculations. When a dynamic system is forced and dissipative all the trajectories tend toward a bounded set of zero volume - often a strange attractor with a fractal dimension. The stochastic dynamic equations can directly reveal the statistical moments of the system, but their direct solution is inefficient, and they are not a closed set. The power of the combined method is that the time averaged Monte Carlo moments will agree exactly with equations described by the left hand side of the full stochastic dynamic equations set to zero - no closure is required. Every equation expresses an exact relationship among the variables. One is able to delve far deeper into the nature of the nonlinear systems. This tutorial exposition offers the tools for the past nonlinear modeling efforts in the traditional physical sciences and in various complex modeling problems in new fields of biology and health sciences.