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Regular version of the site

Article

Homoclinic and stable periodic solutions for differential delay equations from physiology

Discrete and Continuous Dynamical Systems. 2018. Vol. 38. No. 7. P. 3637-3661.

A one-parameter family of Mackey-Glass type differential delay equations is considered. The existence of a homoclinic solution for suitable parameter value is proved. As a consequence, one obtains stable periodic solutions for nearby parameter values. An example of a nonlinear functions is given, for which all sufficient conditions of our theoretical results can be verified numerically. Numerically computed solutions are shown.