### Computer-assisted proof of a periodic solution in a nonlinear feedback DDE

#### Abstract

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.

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.

#### Keywords

Topological degree; dynamical systems; ordinary differential equations

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