- PII
- 10.31857/S037406412304012X-1
- DOI
- 10.31857/S037406412304012X
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 59 / Issue number 4
- Pages
- 563-566
- Abstract
- Asymptotic methods are used to study solutions of a modified logistic delay equation containing a large parameter. A result on the existence and stability of a relaxation cycle is given.
- Keywords
- Date of publication
- 19.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 10
References
- 1. Murray J.D. Mathematical Biology II. Spatial Models and Biomedical Applications. Interdisciplinary Applied Mathematics. V. 18. New York, 2003.
- 2. Wu J. Theory and Applications of Partial Functional Differential Equations. Applied Mathematical Sciences. V. 119. New York, 1996.
- 3. Kuang Y. Delay Differential Equations with Applications in Population Dynamics. Mathematics in Science and Engineering. V. 191. Boston, 1993.
- 4. Wright E.M. A non-linear difference-differential equation // J. f\\"ur die reine und angewandte Mathematik. 1955. Bd. 194. S. 66-87.
- 5. Кащенко С.А., Логинов Д.О. Оценка области глобальной устойчивости состояния равновесия логистического уравнения с запаздыванием // Изв. вузов. Математика. 2020. № 9. C. 39-55.
- 6. May R.M. Stability and Complexity in Model Ecosystems. Princeton, 1974.
- 7. Кащенко С.А. Бифуркации в логистическом уравнении с запаздыванием и малыми возмущениями // Изв. вузов. Математика. 2020. № 10. C. 47-64.
- 8. Oster G., Guckenheimer J. Bifurcation phenomena in population models // The Hopf Bifurcation and Its Applications. Appl. Math. Sci. New York, 1976. V. 19. P. 327-353.
- 9. Kashchenko S.A. Asymptotics of the solutions of the generalized Hutchinson equation // Automatic Control and Computer Sciences. 2013. V. 47. P. 470-494.
- 10. Кащенко С.А. Динамика моделей на основе логистического уравнения с запаздыванием. М., 2020.
- 11. Edwards R.E. Functional Analysis. Theory and Applications. New York, 1965.
- 12. Кащенко С.А. Периодические решения нелинейных уравнений, обобщающих логистические уравнения с запаздыванием // Мат. заметки. 2017. Т. 102. С. 216-230.