| Full text | |
| Author(s): |
Carvalho, Yagor Romano
;
Gouveia, Luiz F. S.
;
Makarenkov, Oleg
Total Authors: 3
|
| Document type: | Journal article |
| Source: | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION; v. 143, p. 10-pg., 2025-02-07. |
| Abstract | |
In this paper, we study the number of isolated crossing periodic orbits, so-called crossing limit cycles, for a class of piecewise smooth Kolmogorov systems defined in two zones separated by a straight line. In particular, we study the number of crossing limit cycles of small amplitude. They are all nested and surround one equilibrium point or a sliding segment. We denote by .A4 (n) the maximum number of crossing limit cycles bifurcating from the equilibrium point via a degenerate Hopf bifurcation for a piecewise smooth Kolmogorov systems of degree n = m+ 1. We make a progress towards the determination of the lower bounds MK(n) of crossing limit cycles bifurcating from the equilibrium point via a degenerate Hopf bifurcation for a piecewise smooth Kolmogorov system of degree n. Specifically, we shot that .A4(2) >= 1, .A4(3) >= 12, and .A4 particular, we show at least one crossing limit cycle in Palomba's economics (4) >= 18. In model, considering it from a piecewise smooth point of view. To our knowledge, these are the best quotes of limit cycles for piecewise smooth polynomial Kolmogorov systems in the literature. (AU) | |
| FAPESP's process: | 22/03800-7 - Study of math epidemiological models in piecewise smooth systems and regularization |
| Grantee: | Yagor Romano Carvalho |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| FAPESP's process: | 22/03801-3 - Lower bounds for local cyclicity for Kolmogorov systems on planar piecewise vector fields |
| Grantee: | Luiz Fernando da Silva Gouveia |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| FAPESP's process: | 20/04717-0 - Dynamical systems with symmetries and implicit differential equations |
| Grantee: | Luiz Fernando da Silva Gouveia |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 21/14695-7 - Limit cycles, regularization and period function of piecewise smooth planar systems. |
| Grantee: | Yagor Romano Carvalho |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |