Geodesic
Features of the problem on synchronization of two van der Pol--Duffing oscillators in the case of a direct connection and the presence of symmetry
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 1, Tome 220 (2023), pp. 49-60

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Two coupled van der Pol–Duffing oscillators are considered in the case of direct symmetric coupling. We show that synchronization of oscillations (i.e., the presence of stable limit cycles) is typical for self-oscillating systems. Asymptotic formulas for the corresponding solutions are obtained. It is found that the behavior of solutions is not affected by the presence or absence of resonances of eigenfrequencies in the linearized problem.
Keywords: van der Pol–Duffing oscillator, feedforward, synchronization, normal form, resonance of eigenfrequencies, stability, self-oscillations. 
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     author = {D. A. Kulikov},
     title = {Features of the problem on synchronization of two van der {Pol--Duffing} oscillators in the case of a direct connection and the presence of symmetry},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {49--60},
     publisher = {mathdoc},
     volume = {220},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_220_a6/}
}
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D. A. Kulikov. Features of the problem on synchronization of two van der Pol--Duffing oscillators in the case of a direct connection and the presence of symmetry. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 1, Tome 220 (2023), pp. 49-60. http://geodesic.mathdoc.fr/item/INTO_2023_220_a6/