Computing probability density of the first passage time for state transition in stochastic dynamical systems driven by Brownian motions: A singular integral method
Nonlinear dynamical systems, such as climate systems, often switch from one metastable state to another when subject to noise. The first occurrence of such state transition, which is usually characterized by the first passage time, has gained enormous interest in many engineering and scientific fiel...
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| Published in | Chaos (Woodbury, N.Y.) Vol. 34; no. 1 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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United States
American Institute of Physics
01.01.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1054-1500 1089-7682 1089-7682 |
| DOI | 10.1063/5.0180511 |
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| Abstract | Nonlinear dynamical systems, such as climate systems, often switch from one metastable state to another when subject to noise. The first occurrence of such state transition, which is usually characterized by the first passage time, has gained enormous interest in many engineering and scientific fields. We develop an efficient numerical method to compute the probability density of the first passage time for state transitions in stochastic dynamical systems driven by Brownian motions. The proposed method involves solving a singular integral equation, which determines probability density of the first passage time. Some numerical examples, with application to a simplified thermohaline circulation system, are provided to illustrate and verify the proposed method. |
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| AbstractList | Nonlinear dynamical systems, such as climate systems, often switch from one metastable state to another when subject to noise. The first occurrence of such state transition, which is usually characterized by the first passage time, has gained enormous interest in many engineering and scientific fields. We develop an efficient numerical method to compute the probability density of the first passage time for state transitions in stochastic dynamical systems driven by Brownian motions. The proposed method involves solving a singular integral equation, which determines probability density of the first passage time. Some numerical examples, with application to a simplified thermohaline circulation system, are provided to illustrate and verify the proposed method. Nonlinear dynamical systems, such as climate systems, often switch from one metastable state to another when subject to noise. The first occurrence of such state transition, which is usually characterized by the first passage time, has gained enormous interest in many engineering and scientific fields. We develop an efficient numerical method to compute the probability density of the first passage time for state transitions in stochastic dynamical systems driven by Brownian motions. The proposed method involves solving a singular integral equation, which determines probability density of the first passage time. Some numerical examples, with application to a simplified thermohaline circulation system, are provided to illustrate and verify the proposed method.Nonlinear dynamical systems, such as climate systems, often switch from one metastable state to another when subject to noise. The first occurrence of such state transition, which is usually characterized by the first passage time, has gained enormous interest in many engineering and scientific fields. We develop an efficient numerical method to compute the probability density of the first passage time for state transitions in stochastic dynamical systems driven by Brownian motions. The proposed method involves solving a singular integral equation, which determines probability density of the first passage time. Some numerical examples, with application to a simplified thermohaline circulation system, are provided to illustrate and verify the proposed method. |
| Author | Sun, Thomas Sun, Xu Yang, Fang |
| Author_xml | – sequence: 1 givenname: Xu surname: Sun fullname: Sun, Xu organization: School of Mathematics and Statistics, Huazhong University of Science and Technology – sequence: 2 givenname: Fang surname: Yang fullname: Yang, Fang organization: Basic Department, Information Engineering University – sequence: 3 givenname: Thomas surname: Sun fullname: Sun, Thomas organization: 3ISA Wuhan Wenhua School, Wuhan 430119, Hubei, China |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/38166172$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1103/PhysRevE.99.052203 10.1063/5.0037083 10.1088/1367-2630/ab81b9 10.1515/mcma.1996.2.2.93 10.1063/1.5116626 10.1175/1520-0485(1993)023<0039:SAVOTT>2.0.CO;2 10.1175/1520-0485(2002)032<2072:SOCRBN>2.0.CO;2 10.1175/1520-0485(2000)030<1891:NITIAS>2.0.CO;2 10.1175/1520-0485(1994)024<1911:ASBMOS>2.0.CO;2 10.1016/j.quascirev.2014.09.007 10.1007/s11071-023-08636-y 10.1063/5.0006626 |
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| Snippet | Nonlinear dynamical systems, such as climate systems, often switch from one metastable state to another when subject to noise. The first occurrence of such... |
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| SubjectTerms | Brownian motion Density Dynamical systems Metastable state Nonlinear systems Numerical methods Probability theory Singular integral equations Thermohaline circulation |
| Title | Computing probability density of the first passage time for state transition in stochastic dynamical systems driven by Brownian motions: A singular integral method |
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