Geodesic
Dynamics of the mathematical model of phase-locked systems with delay
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 23 (2021) no. 1, pp. 28-42

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In the article, the conditions for the existence of limit cycles of the first kind are obtained for self-tuning systems with delay, which, in turn, determine the conditions for the occurrence of hidden synchronization modes in such systems. The principle of the proof is based on constructing a positively invariant toroidal set using two cylindrical surfaces, whose boundaries are determined by the limit cycles of a system of the second-order differential equations. Using the results obtained in the article for limit cycles, the possibility of using the curvature of the cycle for a comparative analysis of the proximity of the cycles of phase and non-phase systems, as well as for determining the mode of hidden synchronization, is shown.
Keywords: system of differential equations, phase system, limit cycles of the first kind, latent synchronization, multistability, fixed point, shift operator, rotation of a vector field, cycle curvature. 
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S. S. Mamonov; I. V. Ionova; A. O. Harlamova. Dynamics of the mathematical model of phase-locked systems with delay. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 23 (2021) no. 1, pp. 28-42. http://geodesic.mathdoc.fr/item/SVMO_2021_23_1_a1/