| Full text | |
| Author(s): |
Gouveia, Luiz F. S.
;
Queiroz, Lucas
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 530, n. 1, p. 16-pg., 2024-02-01. |
| Abstract | |
We consider quadratic three-dimensional differential systems having a Hopf singular point. We study their cyclicity when the singular point is a center on the center manifold using higher-order developments of the Lyapunov constants. As a result, we make a chart of the cyclicity by establishing the lower bounds for several known systems in the literature, including the Rossler, Lorenz, and Moon-Rand systems. Moreover, we construct an example of a jerk system to obtain 12 limit cycles bifurcating from the center, which is a new lower bound for three-dimensional quadratic systems. & COPY; 2023 Elsevier Inc. All rights reserved. (AU) | |
| 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: | 19/13040-7 - Nilpotent centers on the center manifolds |
| Grantee: | Lucas Queiroz Arakaki |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 21/14450-4 - Bifurcation phenomena in time of differential equations |
| Grantee: | Lucas Queiroz Arakaki |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |