Computer-assisted proof of a periodic solution in a nonlinear feedback DDE
Keywords
Topological degree, dynamical systems, ordinary differential equationsAbstract
In this paper, we rigorously prove the existence of a non-trivial periodic orbit for the nonlinear DDE: $x'(t) = - K \sin(x(t-1))$ for $K=1.6$. We show that the equations for the Fourier coefficients have a solution by computing the local Brouwer degree. This degree can be computed by using a homotopy, and its validity can be proved by checking a finite number of inequalities. Checking these inequalities is done by a computer program.Downloads
Published
2009-06-01
How to Cite
1.
ZALEWSKI, Mikołaj. Computer-assisted proof of a periodic solution in a nonlinear feedback DDE. Topological Methods in Nonlinear Analysis. Online. 1 June 2009. Vol. 33, no. 2, pp. 373 - 393. [Accessed 26 April 2024].
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