Approximation of limit cycle of differential systems with variable coefficients

Masakazu Onitsuka

Archivum Mathematicum (2023)

  • Issue: 1, page 85-97
  • ISSN: 0044-8753

Abstract

top
The behavior of the approximate solutions of two-dimensional nonlinear differential systems with variable coefficients is considered. Using a property of the approximate solution, so called conditional Ulam stability of a generalized logistic equation, the behavior of the approximate solution of the system is investigated. The obtained result explicitly presents the error between the limit cycle and its approximation. Some examples are presented with numerical simulations.

How to cite

top

Onitsuka, Masakazu. "Approximation of limit cycle of differential systems with variable coefficients." Archivum Mathematicum (2023): 85-97. <http://eudml.org/doc/298978>.

@article{Onitsuka2023,
abstract = {The behavior of the approximate solutions of two-dimensional nonlinear differential systems with variable coefficients is considered. Using a property of the approximate solution, so called conditional Ulam stability of a generalized logistic equation, the behavior of the approximate solution of the system is investigated. The obtained result explicitly presents the error between the limit cycle and its approximation. Some examples are presented with numerical simulations.},
author = {Onitsuka, Masakazu},
journal = {Archivum Mathematicum},
keywords = {approximate solution; variable coefficients; generalized logistic equation; conditional Ulam stability; limit cycle},
language = {eng},
number = {1},
pages = {85-97},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Approximation of limit cycle of differential systems with variable coefficients},
url = {http://eudml.org/doc/298978},
year = {2023},
}

TY - JOUR
AU - Onitsuka, Masakazu
TI - Approximation of limit cycle of differential systems with variable coefficients
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 1
SP - 85
EP - 97
AB - The behavior of the approximate solutions of two-dimensional nonlinear differential systems with variable coefficients is considered. Using a property of the approximate solution, so called conditional Ulam stability of a generalized logistic equation, the behavior of the approximate solution of the system is investigated. The obtained result explicitly presents the error between the limit cycle and its approximation. Some examples are presented with numerical simulations.
LA - eng
KW - approximate solution; variable coefficients; generalized logistic equation; conditional Ulam stability; limit cycle
UR - http://eudml.org/doc/298978
ER -

References

top
  1. Anderson, D.R., Onitsuka, M., 10.1007/s00025-022-01671-y, Results Math. 77 (2022), 23, Paper No. 136. (2022) MR4420286DOI10.1007/s00025-022-01671-y
  2. Benterki, R., Jimenez, J., Llibre, J., Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibria separated by reducible cubics, Electron. J. Qual. Theory Differ. Equ. 2021 (2021), 38 pp., Paper No. 69. (2021) MR4389338
  3. Boukoucha, R., Limit cycles explicitly given for a class of a differential systems, Nonlinear Stud. 28 (2) (2021), 375–387. (2021) MR4328117
  4. Castro, L.P., Simões, A.M., 10.2298/FIL2113391C, Filomat 35 (13) (2021), 4391–4403. (2021) MR4365541DOI10.2298/FIL2113391C
  5. Deepa, S., Bowmiya, S., Ganesh, A., Govindan, V., Park, C., Lee, J., 10.3934/math.2022278, AIMS Math. 7 (4) (2022), 4992–5014. (2022) MR4357984DOI10.3934/math.2022278
  6. Devi, A., Kumar, A., Hyers-Ulam stability and existence of solution for hybrid fractional differential equation with p -Laplacian operator, Chaos Solitons Fractals 156 (2022), 8 pp., Paper No. 111859. (2022) MR4379223
  7. Diab, Z., Guirao, J.L.G., Vera, J.A., 10.1080/14689367.2021.1993144, Dyn. Syst. 37 (1) (2022), 1–8. (2022) MR4408073DOI10.1080/14689367.2021.1993144
  8. Fečkan, M., Li, Q., Wang, J., 10.1007/s00605-021-01618-5, Monatsh. Math. 197 (3) (2022), 419–434. (2022) MR4389128DOI10.1007/s00605-021-01618-5
  9. Galias, Z., Tucker, W., The Songling system has exactly four limit cycles, Appl. Math. Comput. 415 (2022), 8 pp., Paper No. 126691. (2022) MR4327335
  10. Gong, S., Han, M., An estimate of the number of limit cycles bifurcating from a planar integrable system, Bull. Sci. Math. 176 (2022), 39 pp., Paper No. 103118. (2022) MR4395271
  11. Huang, J., Li, J., On the number of limit cycles in piecewise smooth generalized Abel equations with two asymmetric zones, Nonlinear Anal. Real World Appl. 66 (2022), 17 pp., Paper No. 103551. (2022) MR4389045
  12. Jung, S.-M., Ponmana Selvan, A., Murali, R., 10.7153/jmi-2021-15-80, J. Math. Inequal. 15 (3) (2021), 1201–1218. (2021) MR4364669DOI10.7153/jmi-2021-15-80
  13. Kelley, W.G., Peterson, A.C., The Theory of Differential Equations: Classical and Qualitative, Springer, New York, 2010, Second Edition, Universitext. (2010) MR2640364
  14. Li, J., Han, M., Planar integrable nonlinear oscillators having a stable limit cycle, J. Appl. Anal. Comput. 12 (2) (2022), 862–867. (2022) MR4398697
  15. Nam, Y.W., 10.1016/j.amc.2019.03.033, Appl. Math. Comput. 356 (2019), 119–136. (2019) MR3933980DOI10.1016/j.amc.2019.03.033
  16. Onitsuka, M., Approximate solutions of generalized logistic equation, submitted. 
  17. Onitsuka, M., Conditional Ulam stability and its application to the logistic model, Appl. Math. Lett. 122 (2021), 7 pp., Paper No. 107565. (2021) MR4296927
  18. Onitsuka, M., 10.3934/mbe.2022129, Math. Biosci. Eng. 19 (3) (2022), 2819–2834. (2022) MR4364436DOI10.3934/mbe.2022129
  19. Onitsuka, M., El-Fassi, Iz., 10.1016/j.amc.2022.127205, Appl. Math. Comput. 428 (2022), 13 pp., Paper No. 127205. (2022) MR4421006DOI10.1016/j.amc.2022.127205
  20. Sugie, J., Ishibashi, K., Limit cycles of a class of Liénard systems derived from state-dependent impulses, Nonlinear Anal. Hybrid Syst. 45 (2022), 16 pp., Paper No. 101188. (2022) MR4399231

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.