2015-№3(48) Article 17

Z.S. Svirina

M.T. Terekhin and the qualitative theory of differential equations. P.147-158.

UDC 51(092.2)

In the essay lays out the facts of the employment biography and main stages of scientific work, the outstanding specialist in the field of qualitative theory of differential equations, founder of the scientific school, the first Honorary Professor of Ryazan state University University of a name of S.A. Esenin.

Teryokhin M.T., RSU name S.A. Esenin, mathematics differential equations, scientific school, local history

Bibliography:

1. Teryokhin, M.T. Povorot polya napravlenij i razyskanie predel’nykh tsiklov [Rotate of the directional field and the release of limit cycles] [Text] // Sbornik statej po kachestvennoj teorii differentsial’nykh uravnenij. Uchenye zapiski. — Collection of articles on the qualitative theory of differential equations. Scientific notes. — M.: Higher school, 1966. — Vol. 41. — P. 48–53.
2. Teryokhin, M.T. Dvizhenie predel’nykh tsiklov pri izmenenii parametra [Movement of limit cycles in the parameter change] [Text] // Sbornik statej po kachestvennoj teorii differentsial’nykh uravnenij. Uchenye zapiski. — Collection of articles on the qualitative theory of differential equations. Scientific notes. — Ryazan: Ryazan State Pedagogical Institute, 1971. — T. 102. — P. 109–116.
3. Teryokhin, M.T. O resheniyakh differentsial’nykh uravnenij s otklonyayushhimsya argumentom [Of the solutions of differential equations with deviating argument] [Text] // Differentsial’nye uravneniya. —Differential equations. — 1983. — Vol. 19, N. 4. — P. 597–601.
4. Teryokhin, M.T. O suschestvovanii nepodvizhnoy tochki odnogo nelineynogo operatora [About the existence of a fixed point of one nonlinear operator] [Text] // Differentsial’nye uravneniya. — Differential equations. — 1984. — Vol. 20, N 9. — P. 1561–1565.
5. Teryokhin, M.T. Bifurkatsiya periodicheskogo resheniya sistemy obyknovennykh differentsial’nykh uravneniy [The bifurcation of periodic solution of ordinary differential system] [Text] // Ukrainskiy matematicheskiy zhurnal. — Ukrainian mathematical journal. — 1986. — Vol. 38, N 3. — P. 390–393.
6. Teryokhin, M.T. Usloviya susсhestvovaniya osobogo znacheniya parametra sistemy obyknovennykh differentsial’nykh uravneniy [The existence conditions of the special parameter of ordinary differential system] [Text] // Differentsial’nye uravneniya. — Differential equations. — 1991. — Vol. 27, N 2. — P. 238–242.
7. Teryokhin, M.T. Suschestvovanie bifurkatsionnogo znacheniya parametra sistemy differentsial’nykh uravneniy s otklonyayuschimsya argumentom [The existence of the bifurcation value of parameter system of the differential equations with divergent argument] [Text] // Ukrainskiy matematicheskiy zhurnal. — Ukrainian mathematical journal. — 1997. — Vol. 49, N 6. — P. 799–805.
8. Teryokhin, M.T. Bifurkatsiya periodicheskikh resheniy funktsional’no-differen-tsial’nykh uravneniy [The bifurcation of periodic solutions of functional differential equations] [Text] // Izvestiya vuzov. Matematika. — Proceedings of the universities. Mathematics. — 1999. — N 10/449. — P. 37–42.
9. Teryokhin, M.T. Nenulevye periodicheskie resheniya neavtonomnykh sistem differentsial’nykh uravneniy vtorogo poryadka [Nonnull periodic solutions of nonautonomous systems of differential equations of the second order] [Text] // Ukrainskiy matematicheskiy zhurnal. — Ukrainian mathematical journal. — 1994. — Vol. 46, N 6. — P. 754–759.
10. Teryokhin, M.T. Periodicheskie resheniya sistemy differentsial’nykh uravneniy s kusochno-postoyannoy matritsey linejnogo priblizheniya [Periodic solutions of the systems of the differential equations with piecewise constant matrix of the linear approximation] [Text] // Differentsial’nye uravneniya. — Differential equations. — 1997. — Vol. 33, N 6. — P. 856–857.
11. Teryokhin, M.T. Periodicheskie resheniya sistemy Resslera [Periodic solutions of the Ressler system] [Text] // Izvestiya vuzov. Matematika. — Proceedings of the universities. Mathematics. — 1999. — N 8/447. — P. 70–73.
12. Teryokhin, M.T. Nenulevye periodicheskie resheniya neavtonomnoy sistemy obyknovennykh differentsial’nykh uravneniy [Nonnull periodic solutions of the nonautonomous system of ordinary differential equations] [Text] // Izvestiya vuzov. Matematika. — Proceedings of the universities. Mathematics. — 2002. — N 6/481. — P. 63–68.
13. Teryokhin, M.T. Metod variatsii promezhutochnoy tochki dlya issledovaniya upravlyaemosti sistemy differentsial’nykh uravneniy [The method of variation of the intermediate point for the study of control systems of differential equations] [Text] // Differentsial’nye uravneniya (kachestvennaya teoriya): mezhvuzovskiy sbornik nauchnykh trudov. — Differential equations (qualitative theory): interuniversity collection of scientific papers. — Ryazan, 1994. — P. 116–124.
14. Teryokhin, M.T. Upravlyaemost’ sistemy tipa «khischnik-zhertva» [Controllability of a system the “predator-prey”] [Text] // Trudy Srednevolzhskogo matematicheskogo obschestva. — Proceedings of Middle Volga Mathematical Society. — Saransk: SVMO, 1998. — Vol. 1, N 1. — P. 77–87.
15. Teryokhin, M.T. Ob ustoychivosti upravleniya po parametru [About the stability of fixed value control] [Text] // Izvestiya vuzov. Matematika. — Proceedings of the universities. Mathematics. — 2000. — N 9/460. — P. 38–46.
16. Teryokhin, M.T. O lokal’noy upravlyaemosti nelineynoy sistemy differentsial’nykh uravneniy i usloviyakh lokal’noy optimal’nosti upravleniya [The local controllability of nonlinear differential equations system about and the conditions of local optimality of control] [Text] // Trudy Srednevolzhskogo matematicheskogo obschestva. — Proceedings of Middle Volga Mathematical Society. — 2006. — Vol. 8, N 1. — P. 109–115.
17. Teryokhin, M.T. Upravlyaemost’ linejnoy sistemy differentsial’nykh uravneniy s peremennymi koehffitsientami [Controllability by linear system of the differential equation with variable coefficients] [Text] // Vestnik RАEN. Differentsial’nye uravneniya. — Bulletin of Russian Academy of Natural Sciences. Differential equations. — 2013. — Vol. 13, N 4. — P. 63–75.
18. Teryokhin, M.T. Issledovanie upravlyaemoy sistemy differentsial’nykh uravneniy s avtomaticheskoy obratnoy svyaz’yu [The research of controllable system of the differential equations with automatic feedback] [Text] // Vestnik RАEN. Differentsial’nye uravneniya. — Bulletin of Russian Academy of Natural Sciences. Differential equations. — 2014. — Vol. 14, N 5. — P. 70–75.
19. Teryokhin, M.T. O malykh periodicheskikh resheniyakh sistem obyknovennykh differentsial’nykh uravneniy [About small periodic solutions of the systems of ordinary differential equations] [Text] // Differentsial’nye uravneniya. — Differential Equations. — 1999. — Vol. 35, N 6. — P. 858–859.
20. Teryokhin M.T. Suschestvovanie malykh periodicheskikh resheniy nelineynykh sistem obyknovennykh differentsial’nykh uravneniy [The existence of small periodic solutions of the nonlinear ordinary differential equations system] [Text] // Ukrainskij matematicheskij zhurnal. — Ukrainian mathematical journal. — 2001. — Vol. 53, N 5. — P. 680–687.
21. Teryokhin, M.T. Predel’nye tsikly sistemy differentsial’nykh uravneniy vtorogo poryadka. Metod malykh form. [Boundary cycles of system of differential equations of the second order. The method of small forms] [Text] // Izvestiya vuzov. Matematika. — Proceedings of the universities. Mathematics. — 2009. — N 8.
22. Teryokhin, M.T. Nenulevye periodicheskie resheniya odnoy nelineynoy sistemy differentsial’nykh uravneniy Mat’e [Nonnull periodic solutions of one nonlinear system of the Mathieu equation] [Text] // Bulletin of the Ryazan State University named after S.A. Yesenin. — Ryazan’, 2008. — N 4/21.
23. Teryokhin, M.T. Periodicheskie resheniya sistemy differentsial’nykh uravneniy Khilla [The periodic solutions of systems of the differential Hill equations] [Text] // Izvestiya RАEN. Differentsial’nye uravneniya. — Proceedings of Russian Academy of Natural Sciences. Differential equations. — 2009. — N 14. — P. 117–131.
24. Teryokhin, M.T. Susсhestvovanie nenulevykh periodicheskikh resheniy u osobogo klassa sistem differentsial’nykh uravneniy s parametrom [The existence of nonnull periodic solutions of a special class of systems of differential equations with parameter] [Text] / M.T. Teryokhin, O.V. Baeva // Vestnik Ryazanskogo gosudarstvennogo universiteta imeni S.А. Yesenina. — Bulletin of the Ryazan State University named after S.A. Yesenin. — 2007. — N 3. — P. 77–97.
25. Teryokhin, M.T. Nenulevye periodicheskie resheniya nelinejnykh sistem obyknovennykh differentsial’nykh uravneniy s osobennoy matritsey pri proizvodnykh [Nonnull periodic solutions of the nonlinear systems of the ordinary differential equations with singular matrix at derivatives] [Text] // Differentsial’nye uravneniya. — Differential Equations. — 2003. — Vol. 39, N 12. — P. 1645–1653.
26. Teryokhin, M.T. Periodicheskie resheniya nelinejnykh sistem differentsial’nykh uravneniy s postoyannym otkloneniem [Periodic solutions of the nonlinear systems of differential equations with fixed deviation] [Text] // Trudy Srednevolzhskogo matematicheskogo obschestva. — Proceedings of Middle Volga Mathematical Society. — 2005. — Vol. 7, N 1. — P. 51–59.
27. Teryokhin, M.T. Malye periodicheskie resheniya nelinejnykh sistem s postoyannym otkloneniem [Small periodic solutions of the nonlinear systems with fixed deviation] [Text] // Izvestiya vuzov. Matematika. — Proceedings of the universities. Mathematics. — 2008. — N 6.
28. Teryokhin, M.T. Ob usloviyakh razreshimosti operatornykh uravneniy [About the conditions of tractability of operator equations] [Text] // Izvestiya RАEN. Differentsial’nye uravneniya. — Bulletin of Russian Academy of Natural Sciences. Differential equations. — 2006. — N 10. — P. 56–66.
29. Teryokhin, M.T. Kvaziperiodicheskie rezhimy v matematicheskikh modelyakh s malym otkloneniem [Quasiperiodic modes in the symbolic models with small deviate] [Text] // Bulletin of the Ryazan State University named for S.A. Yesenin. — 2006. — N 1. — P. 140–159.
30. Teryokhin, M.T. Kvaziperiodicheskie po fazovoy peremennoy resheniya parabo-licheskogo uravneniya s parametrom [Quasiperiodic solutions of parabolic equation with parameter of the phase variable] [Text] // Trudy Srednevolzhskogo matematicheskogo obschestva. — Proceedings of Middle Volga Mathematical Society. — 2008. — Vol. 10, N 2.
31. Teryokhin, M.T. Nenulevye resheniya dvukhtochechnoy kraevoy periodicheskoy zadachi dlya differentsial’nykh uravneniy s maksimumami [Nonnull solutions of the two-point boundary value periodic problem for the differential equations with maxima] [Text] // Izvestiya vuzov. Matematika. — Proceedings of the universities. Mathematics. — 2010. — N 6. — P. 52–63.
32. Teryokhin, M.T. Nelokal’noe issledovanie odnoy matematicheskoy modeli upravleniya investitsionnym portfelem [Nonlocal research of one symbolic model of portfolio management] [Text] // Izvestiya RАEN. Differentsial’nye uravneniya. — Bulletin of Russian Academy of Natural Sciences. Differential equations. — 2011. — N 16. — P. 102–118.
33. Teryokhin, M.T. Issledovanie matematicheskoy modeli razvitiya mnogosektornoy ekonomiki [The research of symbolic model of multi-sector economy development] [Text] // Bulletin of RSREA. — Ryazan’, 2006. — Ed. 18. — P. 108–115.
34. Teryokhin, M.T. Usloviya rynochnogo ravnovesiya [The terms of market equilibrium] [Text] // Vestnik Ryazanskogo gosudarstvennogo universiteta imeni S.А. Yesenina. — Bulletin of the Ryazan State University named for S.A. Yesenin. — Ryazan’, 2011. — N 4/33. — P. 167–177.
35. Teryokhin, M.T. Matematicheskie metody issledovaniya nekotorykh problem franchayzingovoy sistemy [Mathematical methods for studying some problems of franchising system] [Text] // Bulletin of the Ryazan State University named for S.A. Yesenin. — Ryazan’, 2013. — N 4/41. — P. 143.