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Applied symbolic dynamics: attractors and filtrations
Stability of symmetric periodic solutions with small amplitude of $\dot x(t)=\alpha f(x(t), x(t-1))$
| 1. | Mathematisches Institut der Universität Giessen, Arndtstrasse 2, 35392 Giessen, Germany |
| 2. | Department of Mathematics, Pennsylvania State University, P.O. Box PSU, Lehman, PA 18627, United States |
$\dot x(t) =\alphaf(x(t), x(t-1))$
where $\alpha$ is a positive parameter and the nonlinearity $f$ satisfies the symmetry conditions $f(-u, v) = -f(u,-v) = f(u, v).$ We establish the existence and stability properties for such periodic solutions with small amplitude.
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