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An Approach to Nonlinear Oscillation...

Byun, Jaeseung,

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An Approach to Nonlinear Oscillations Through Randomization /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An Approach to Nonlinear Oscillations Through Randomization // Jaeseung Byun.
作者:	Byun, Jaeseung,
面頁冊數:	1 electronic resource (119 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
Contained By:	Dissertations Abstracts International86-03B.
標題:	Mechanical engineering. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30990796
ISBN:	9798384451594

An Approach to Nonlinear Oscillations Through Randomization /
Byun, Jaeseung,

An Approach to Nonlinear Oscillations Through Randomization /Jaeseung Byun. - 1 electronic resource (119 pages)

Source: Dissertations Abstracts International, Volume: 86-03, Section: B.

In this thesis, a novel investigation of deterministic nonlinear systems is presented. When autonomous dynamical systems are randomized by white-noise excitation, their behaviors are governed by diffusion equations. The core idea behind the method of randomization involves replacing a nonlinear ordinary differential equation of motion by a linear partial differential equation of diffusion.Exact analytical solutions are feasible for only a limited number of nonlinear systems. However, some nonlinear systems, which are difficult to analyze using deterministic methods, possess stationary diffusion equations with exact solutions. These diffusion responses provide deeper insights into the qualitative behaviors of nonlinear systems, such as stability at multiple equilibria, limit cycles, and bifurcations. To demonstrate the potential and feasibility of randomization, numerous nonlinear oscillators are considered. When both the deterministic systems and the associated randomized systems can be analyzed, there is complete agreement in their qualitative properties. Furthermore, some example systems inaccessible through deterministic approaches can be readily examined using randomization, suggesting that randomization could be an alternative tool for investigating nonlinear oscillations.

English

ISBN: 9798384451594Subjects--Topical Terms:

649730
Mechanical engineering.
Subjects--Index Terms:

Fokker-Planck equation

An Approach to Nonlinear Oscillations Through Randomization /
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520 $a In this thesis, a novel investigation of deterministic nonlinear systems is presented. When autonomous dynamical systems are randomized by white-noise excitation, their behaviors are governed by diffusion equations. The core idea behind the method of randomization involves replacing a nonlinear ordinary differential equation of motion by a linear partial differential equation of diffusion.Exact analytical solutions are feasible for only a limited number of nonlinear systems. However, some nonlinear systems, which are difficult to analyze using deterministic methods, possess stationary diffusion equations with exact solutions. These diffusion responses provide deeper insights into the qualitative behaviors of nonlinear systems, such as stability at multiple equilibria, limit cycles, and bifurcations. To demonstrate the potential and feasibility of randomization, numerous nonlinear oscillators are considered. When both the deterministic systems and the associated randomized systems can be analyzed, there is complete agreement in their qualitative properties. Furthermore, some example systems inaccessible through deterministic approaches can be readily examined using randomization, suggesting that randomization could be an alternative tool for investigating nonlinear oscillations.
546 $a English
590 $a School code: 0028
650 4 $a Mechanical engineering. $3 649730
650 4 $a Applied physics. $3 3343996
650 4 $a Applied mathematics. $3 2122814
650 4 $a Systems science. $3 3168411
653 $a Fokker-Planck equation
653 $a Forward diffusion equation
653 $a Nonlinear dynamical system
653 $a Random vibration
653 $a Randomization
653 $a Stochastic process
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690 $a 0215
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791 $a Ph.D.
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