Abstract:
We introduce a new object, namely, a system of ordinary differential equations
which is a mathematical model of a ring-like chain of unidirectionally
connected RCL-generators. To study periodic solutions of travelling wave type
of this system, some special tricks are used which reduce the existence and
stability problems for cycles to the investigation of auxiliary delay
equations. Using this approach, we establish that the number of stable
travelling waves simultaneously existing in the chain increases unboundedly
as the number of links of the chain increases, that is, the well-known buffer
phenomenon occurs.
Citation:
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “The buffer phenomenon in ring-like chains of unidirectionally connected generators”, Izv. Math., 78:4 (2014), 708–743
This publication is cited in the following 18 articles:
D. D. Bain, “Periodicheskie resheniya differentsialnogo uravneniya s releinoi nelineinostyu s zapazdyvaniem”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 231, VINITI RAN, M., 2024, 3–12
D.D. Bain, “Variational equation for discontinuous delayed systems”, Partial Differential Equations in Applied Mathematics, 2024, 101034
S. D. Glyzin, E. A. Marushkina, “Algorithms for Asymptotic and Numerical Modeling of Oscillatory Modes in the Simplest Ring of Generators with Asymmetric Nonlinearity”, Aut. Control Comp. Sci., 58:7 (2024), 853
S. D. Glyzin, E. A. Marushkina, “Algoritmy asimptoticheskogo i chislennogo postroeniya kolebatelnykh rezhimov v prosteishem koltse generatorov s nesimmetrichnoi nelineinostyu”, Model. i analiz inform. sistem, 30:2 (2023), 160–169
S. D. Glyzin, A. Yu. Kolesov, “Traveling waves in fully coupled networks of linear oscillators”, Comput. Math. Math. Phys., 62:1 (2022), 66–83
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “On a mathematical model of the repressilator”, St. Petersburg Math. J., 33:5 (2022), 797–828
Glyzin S.D., Kolesov A.Yu., Rozov N.Kh., “A New Approach to Gene Network Modeling”, Autom. Control Comp. Sci., 54:7 (2020), 655–684
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “A self-symmetric cycle in a system of two diffusely connected Hutchinson's equations”, Sb. Math., 210:2 (2019), 184–233
A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “On a Mathematical Model of Biological Self-Organization”, Proc. Steklov Inst. Math., 304 (2019), 160–189
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Quasi-stable solutions of the genetic networks models”, International Conference on Computer Simulation in Physics and Beyond, Journal of Physics Conference Series, 1163, ed. L. Shchur, IOP Publishing Ltd, 2019, UNSP 012070
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Novyi podkhod k modelirovaniyu gennykh setei”, Model. i analiz inform. sistem, 26:3 (2019), 365–404
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Self-excited relaxation oscillations in networks of modified fitzhugh-nagumo oscillators”, Vii International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019, 012018
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Stable relaxation cycle in a bilocal neuron model”, Differ. Equ., 54:10 (2018), 1285–1309
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Quasi-stable structures in circular gene networks”, Comput. Math. Math. Phys., 58:5 (2018), 659–679
V. P. Golubyatnikov, N. E. Kirillova, “On cycles in models of functioning of circular gene networks”, J. Math. Sci., 246:6 (2020), 779–787
A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “Periodic solutions of travelling-wave type in circular gene networks”, Izv. Math., 80:3 (2016), 523–548
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Buffering in cyclic gene networks”, Theoret. and Math. Phys., 187:3 (2016), 935–951
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Avtovolnovye protsessy v koltsevoi neironnoi tsepi s odnonapravlennoi svyazyu”, Model. i analiz inform. sistem, 22:3 (2015), 404–419
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