Computing the optimal path in stochastic dynamical systems CHAOS 26, 083101 (2016)

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in highdimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly imple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higherdimensional spaces.

Original languageEnglish
Article number083101
JournalChaos
Volume26
Issue number8
DOIs
StatePublished - 1 Aug 2016

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Stochastic Dynamical Systems
Optimal Path
dynamical systems
Numerical methods
Dynamical systems
Stochastic systems
Computing
Computational methods
Metastable States
Two-dimensional Systems
metastable state
Numerical Methods
Stochastic Systems
Computational Methods
Lyapunov Exponent
Demonstrate
Analytical Solution
newton
escape
Maximise

Cite this

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title = "Computing the optimal path in stochastic dynamical systems CHAOS 26, 083101 (2016)",
abstract = "In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in highdimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly imple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higherdimensional spaces.",
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Computing the optimal path in stochastic dynamical systems CHAOS 26, 083101 (2016). / Bauver, Martha; Forgoston, Eric; Billings, Lora.

In: Chaos, Vol. 26, No. 8, 083101, 01.08.2016.

Research output: Contribution to journalArticle

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