Liouvillian integrability of a deterministic business cycle model (Q2867063)
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scientific article; zbMATH DE number 6237049
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Liouvillian integrability of a deterministic business cycle model |
scientific article; zbMATH DE number 6237049 |
Statements
10 December 2013
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Darboux polynomial
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exponential factor
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Liouvillian first integral
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deterministic business model
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Liouvillian integrability of a deterministic business cycle model (English)
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The author introduces the following model NEWLINE\[NEWLINE\dot{x}=y,\,\dot{y}=(a-1)y-bx-(a+1)y^{3},NEWLINE\]NEWLINE where \(a>0\) and \(b \geq 0\). A first integral is given when \(b=0\). In the case that \(b \neq 0\), it is shown that the system has no Liouvillian first integrals.
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