A Branching Method for Studying Stability of a Solution to a Delay Differential Equation

A Branching Method for Studying Stability of a Solution to a Delay Differential Equation
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We study stability of antisymmetric periodic solutions to delay differential equations. Weintroduce a one-parameter family of periodic solutions to a special system of ordinary differential equations with a variable period. Conditions for stability of an antisymmetric periodic solution to a delay differential equation are stated in terms of this period function.

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