Wandering solutions of delay equations with sine-like feedback (Q2718315)
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scientific article; zbMATH DE number 1606459
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wandering solutions of delay equations with sine-like feedback |
scientific article; zbMATH DE number 1606459 |
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Wandering solutions of delay equations with sine-like feedback (English)
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19 June 2001
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sine-like feedback
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delay equation
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bifurcation
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periodic solution
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period-doubling bifurcation
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0.8720411
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0.8717175
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0.86861455
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0.8673311
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The paper deals with delay equation \(\dot x(t)= f(x(t-1))\), where \(f\) is a real-valued function. This problem has been motivated by the numerical study of bifurcations of periodic solutions of the equation \(\dot x(t)= -\alpha \sin(x(t-1))\), which exhibits successive period-doubling bifurcations from the second branch as the parameter \(\alpha >0\) is varied. The author develops a framework for the description of erratic behavior of solutions of sine-like delay differential equations, and derives explicitly equations with solutions ``wandering up and down'' between arbitrary prescribed levels.
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