Chaotic behavior in differential equations driven by a Brownian motion (Q640047)
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scientific article; zbMATH DE number 5957028
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chaotic behavior in differential equations driven by a Brownian motion |
scientific article; zbMATH DE number 5957028 |
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Chaotic behavior in differential equations driven by a Brownian motion (English)
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12 October 2011
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The authors examine the chaotic behaviour exhibited by ordinary differential equations having a homoclinic orbit to a saddle point under unbounded random forcing driven by Brownian motion. The approach is `sample-wise', though the need for using the features of the Brownian motion as a whole is noted. Application is made to the Duffing equation and the non-linear pendulum.
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Brownian motion
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Wiener shift
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unbounded stochastic forcing
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chaotic behavior
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topological horseshoe
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Cantor sets
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random Melnikov function
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Duffing equation
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pendulum equation
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