Bifurcation from a heteroclinic solution in differential delay equations

Author:
Hans-Otto Walther

Journal:
Trans. Amer. Math. Soc. **290** (1985), 213-233

MSC:
Primary 34K15; Secondary 58F22

MathSciNet review:
787962

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Abstract: We study a class of functional differential equations with periodic nonlinearity in and in . Such equations describe a state variable on a circle with one attractive rest point (given by the argument of ) and with reaction lag to deviations. We prove that for a certain critical value there exists a heteroclinic solution going from the equilibrium solution to the equilibrium . For , this heteroclinic connection is destroyed, and periodic solutions of the second kind bifurcate. These correspond to periodic rotations on the circle.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0787962-4

Keywords:
Characteristic equation,
saddle point property,
heteroclinic solution,
Poincaré map,
periodic solution of the second kind

Article copyright:
© Copyright 1985
American Mathematical Society