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Reduction method for integrodifferential equations

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Literature Cited

  1. F. Tricomi, “Integrazione di un'equazione differenziale presentasi in electronica,” Ann. Scuola Norm. Sup. Pisa, Sci. Fis. Mat.,2, No. 2, 1–20 (1933).

    Google Scholar 

  2. C. Böhm, “Nuovi criteri di esistenza di soluzione periodiche di una nota equazione differenziale non lineare,” Ann. Mat. Pura Appl.,35, 344–353 (1953).

    Google Scholar 

  3. W. D. Hayes, “On the equation for a damped pendulum under constant torque,” Z. Angew. Math. Phys.,4, No. 5, 398–401 (1953).

    Google Scholar 

  4. E. A. Barabashin and V. A. Tabueva, Dynamical Systems with Cylindrical Phase Space [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  5. L. N. Belyustina, “On an equation, in the theory of electrical machines,” in: In Memory of A. A. Andronov [in Russian], Izd. Akad. Nauk SSSR, Moscow (1955), pp. 173–186.

    Google Scholar 

  6. L. Amerio, “Determinazione delle condizioni di stabilita per gli integrali di un'equazione interessante l'electronica,” Ann. Mat. Pura Appl.,30, 75–90 (1949).

    Google Scholar 

  7. G. Seifert, “On the existence of certain solutions of nonlinear differential equations,” Z. Angew. Math. Phys.,3, No. 6, 468–471 (1952).

    Google Scholar 

  8. V. A. Tabueva, “Estimate of the critical value of the parameter for the differential equation\(\ddot x + \alpha \dot x + f(x) = 0\),” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 227–237 (1958).

    Google Scholar 

  9. M. L. Cartwright, “Some aspects of the theory of nonlinear vibrations,” in: Proceedings of the International Congress of Mathematicians, 1954, Part 3, Groningen-Amsterdam (1956), pp. 71–76.

  10. S. V. Pervachev, “Lock-in range of a phase-synchronized automatic frequency control system,” Radiotekh. Elektron.,8, No. 2, 334–337 (1963).

    Google Scholar 

  11. L. N. Belyustina, V. B. Bykov, K. G. Kiveleva, and V. D. Shalfeev, “On the lock-in value of an AFC system with proportional integrating filter,” Izv. Vyssh. Uchebn. Zaved., Radiofiz.,13, No. 4, 561–567 (1970).

    Google Scholar 

  12. Z. Jelonek, O. Celinsky, and R. Syski, “Pulling effect in synchronized systems,” PIEE, Part IV, February (1954), pp. 108–117.

    Google Scholar 

  13. V. V. Shakhgil'dyan and A. A. Lyakhovkin, Phase-Synchronized Automatic Frequency Control Systems [in Russian], Svyaz', Moscow (1972).

    Google Scholar 

  14. V. V. Shakhgil'dyan and L. N. Belyustina (editors), Phase Synchronization [in Russian], Svyaz', Moscow (1975).

    Google Scholar 

  15. Yu. N. Bakaev, “Influence of delay on synchronization of systems with automatic phase regulation,” Izv. Akad. Nauk SSSR, Ser. Tekh. Kibern., No. 1, 139–143 (1963).

    Google Scholar 

  16. O. R. Rykin and E. I. Yurevich, “Method of harmonic linearization of type II in questions of the stability of a self-propelled gun with periodic nonlinearities,” Tr. Leningr. Politekh. Inst., No. 303, 9–15 (1969).

    Google Scholar 

  17. V. V. Bykov, “Stability of AFC systems with proportional integrating filter and delay,” Izv. Vyssh. Uchebn. Zaved., Radiofiz.,10, No. 3, 447–450 (1967).

    Google Scholar 

  18. Z. Jelonek and C. Cowan, “Synchronized systems with time delay in the loop,” PIEE, Part C, September (1957), pp. 388–397.

  19. B. N. Biswas, P. Banerjee, and A. K. Bhattacharya, “Heterodyne phase-locked loops-revisited,” IEEE Trans. on Communications, COM-25, No. 10, October (1977), pp. 1164–1170.

    Google Scholar 

  20. G. A. Leonov, “Stability and perturbations of phase-synchronized systems,” Sib. Mat. Zh.,16, No. 5, 1031–1052 (1975).

    Google Scholar 

  21. G. A. Leonov, “On a class of dynamical systems with cylindrical phase space,” Sib. Mat. Zh.,17, No. 1, 91–112 (1976).

    Google Scholar 

  22. G. A. Leonov, “The second Lyapunov method in the theory of phase synchronization,” Prikl. Mat. Mekh.,40, No. 2, 238–245 (1976).

    Google Scholar 

  23. V. M. Popov “Absolute stability of nonlinear automatic control systems,” Avtom Telemekh., No. 8, 961–979 (1961).

    Google Scholar 

  24. V. A. Yakubovich, “Frequency conditions for the stability of solutions of integral automatic control equations,” Vestn. Leningr. Univ., No. 7, 109–125 (1967).

    Google Scholar 

  25. A. Kh. Gelig, “Absolute stability of nonlinear controlled systems with distributed parameters,” Avtom. Telemekh.,26, No. 3, 401–409 (1965).

    Google Scholar 

  26. V. M. Popov, Hyperstability of Automatic Systems [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  27. A. Kh. Gelig, “On the stability of nonlinear systems with an infinite number of degrees of freedom,” Prikl. Mat. Mekh.,30, No. 4, 789–794 (1966).

    Google Scholar 

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Authors
  1. G. A. Leonov
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  2. V. B. Smirnova
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Additional information

Leningrad State University, Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 21, No. 4, pp. 112–124, July–August, 1980.

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Leonov, G.A., Smirnova, V.B. Reduction method for integrodifferential equations. Sib Math J 21, 565–575 (1980). https://doi.org/10.1007/BF00995957

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  • DOI: https://doi.org/10.1007/BF00995957

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