A qualitative study of a trigonometric autonomous system (Q1323071)
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scientific article; zbMATH DE number 566445
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A qualitative study of a trigonometric autonomous system |
scientific article; zbMATH DE number 566445 |
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A qualitative study of a trigonometric autonomous system (English)
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9 May 1994
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A qualitative analysis is made of the autonomous system \(\dot x = \sin y\), \(\dot y = - \sin x + d \sin ny\) defined on the torus \(T^ 2 = [-\pi, \pi] \times [-\pi, \pi]\), where \(d \in R\) and \(n\) is a positive integer. It is proved that for \(0 < d \ll I\) the system has at least \(2(n-1)\) limit cycles.
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autonomous system
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torus
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limit cycles
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