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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 2024 Volume 220, Number 2, Pages 396–404 (Mi tmf10661)

Periodic solutions of a differential equation with a discontinuous delayed neutral-type feedback

Yu. A. Yakubiv

Demidov Yaroslavl State University, Yaroslavl, Russia

Abstract: We consider a differential equation with a discontinuous delayed neutral-type feedback. In the phase space, we describe classes of initial functions that depend on a number of parameters. We show that in a certain time, solutions return to an analogous class, possibly with other parameters. The analysis of the change in the parameters allows describing periodic solutions and their stability. We show that infinitely many of stable periodic solutions exist.

Keywords: neutral-type equation, discontinuous delayed feedback, periodic solution.

Received: 15.12.2023
Revised: 21.03.2024

DOI: 10.4213/tmf10661


 English version:
Theoretical and Mathematical Physics, 2024, 220:2, 1402–1409

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© Steklov Math. Inst. of RAS, 2026