SPECIFIED GLOBAL POINCARE–BENDIXSON ANNULUS WITH THE LIMIT CYCLE OF THE RAYLEIGH SYSTEM

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Аннотация

In the work of A. Grin and K. Schneider [1] two algebraic transversal ovals, which form the Poincare–Bendixson annulus

Авторлар туралы

Y. Li

Lanzhou City University

Email: li_liyong120@163.com
China

A. Grin

Yanka Kupala State University of Grodno

Email: grin@grsu.by
Belarus

A. Kuzmich

Yanka Kupala State University of Grodno

Email: kuzmich_av@grsu.by
Belarus

Әдебиет тізімі

  1. Bautin, N.P. and Leontovich, E.A., Metody i priemy kachestvennogo issledovaniia dinamicheskikh sistem na ploskosti (Methods and techniques for qualitative research of dynamic systems on a plane), Moscow: Bukinist, 1990.
  2. Andronov, A.A., Vitt, A.A., and Hajkin, S.E., Teoriia kolebanii (Oscillation theory), Moscow: Fizmatgiz, 1959.
  3. Perko, L. Differential Equations and Dynamical Systems / L. Perko. — New York ; Berlin ; Heidelberg : Springer, 2001. — 555 p.
  4. Rejssig, R., Sansone, G., and Konti, R., Non-Linear Differential Equations of Higher Order, Dordrecht: Springer, 1974.
  5. Lynch, S. Dynamical systems with Applications using Mathematica / S. Lynch. — Boston : Birkh¨auser, 2007. — 585 p.
  6. Flanders, D.A. The limit case of relaxation oscillations / D.A. Flanders, J.J. Stoker // Studies in Nonlinear Vibration Theory ; ed. Howard J. Eckweiler. — New York : New York University, 1946. — P. 51–64.
  7. Schneider, K.R. New approach to study the Van der Pol equation for large damping / K.R. Schneider // Electron. J. Qual. Theory Differ. Equat. — 2018. — V. 8. — P. 1–10.
  8. Gasull, A. Effective construction of Poincar´e–Bendixson regions / A. Gasull, H. Giacomini, M. Grau // J. Appl. Anal. Comp. — 2017. — V. 7. — P. 1549–1569.
  9. Giacomini, H. Transversal conics and the existence of limit cycles / H. Giacomini, M. Grau // J. Math. Anal. Appl. — 2015. — V. 428. — P. 563–586.
  10. Grin, A.A. and Schneider, K.R., Global algebraic Poincar´e–Bendixson annulus for the Van der Pol equation, Differ. Equat., 2022, vol. 58, no. 3, pp. 285–295.
  11. Cherkas, L.A., Dulac function for polynomial autonomous systems on a plane, Differ. Equat., 1997, vol. 33, pp. 692–701.
  12. Cherkas, L.A., Grin, A.A., and Bulgakov, V.I., Konstruktivnye metody issledovaniia predel’nykh tsiklov avtonomnykh sistem vtorogo poriadka (chislenno-algebraicheskii podkhod) (Constructive methods for studying limit cycles of second-order autonomous systems (numerical-algebraic approach)), Grodno: Grodnen. gos. un-t im. Yanki Kupaly, 2013.
  13. Grin, A.A. Location of the limit cycle for a class of Lienard systems by means of Dulac–Cherkas functions / A.A. Grin, K.R. Schneider // Memoirs on Differ. Equat. and Math. Phys. — 2023. — V. 90. — P. 1–11.
  14. Grin, A.A. Global algebraic Poincar´e–Bendixson annulus for the Rayleigh equation / A.A. Grin, K.R. Schneider // Electron. J. Qual. Theory Differ. Equat. — 2023. — V. 35. — P. 1–12.
  15. Birkhoff, G. Ordinary Differential Equations / G. Birkhoff, G.-C. Rota. — New York : John Wiley & Sons, 1989. — 416 p.
  16. Rayleigh, J. The Theory of Sound / J. Rayleigh. — New York, 1945. — 520 p.
  17. Georgescu, A. Approximate limit cycles for the Rayleigh model / A. Georgescu, P. Bazavan, M. Sterpu // ROMAI J. — 2008. — V. 4, № 2. — P. 73–80.
  18. Ghaffari, A. On Rayleigh’s nonlinear vibration equation / A. Ghaffari // Proc. Int. Sympos. Non-linear Vibrations. Kiev, 1963. — V. 2. — P. 131–133.
  19. Lopez, M.A. A note on the generalized Rayleigh equation: limit cycles and stability / M.A. Lopez, R. Martinez // J. Math. Chem. — 2013. — V. 51. — P. 1164–1169.
  20. Palit, A. Comparative study of homotopy analysis and renormalization group methods on Rayleigh and Van der Pol equations / A. Palit, D.P. Datta // Differ. Equat. Dynan. Syst. — 2016. — V. 24. — P. 417–443.
  21. Saha, S. Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators / S. Saha, G. Gangopadhyay, R.D. Shankar // Commun. Nonlin. Sci. Numer. Simul. — 2020. — V. 85. — P. 12.
  22. Tliachev, V.B., Usho, A.D., and Usho, D.S., On periodic solutions of the Rayleigh equation, Izvestiia Saratovskogo universiteta. Novaia seriia. Seriia: Matematika. Mekhanika. Informatika, 2021, vol. 21, no. 2, pp. 173–181.
  23. Grin, A.A. On some classes of limit cycles of planar dynamical systems / A.A. Grin, K.R. Schneider // Dyn. Contin. Discrete Impuls. Syst. Ser. A. Math. Anal. — 2007. — V. 14. — P. 641–656.

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