| Full text | |
| Author(s): |
Gasull, Armengol
;
Rondon, Gabriel
;
da Silva, Paulo Ricardo
Total Authors: 3
|
| Document type: | Journal article |
| Source: | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 23, n. 3, p. 30-pg., 2024-01-01. |
| Abstract | |
In this paper, we are concerned with determining lower bounds of the number of limit cycles for piecewise polynomial holomorphic systems with a straight line of discontinuity. We approach this problem with different points of view. Initially, we study the number of zeros of the first- and second order averaging functions. We also use the Lyapunov quantities to produce limit cycles appearing from a monodromic equilibrium point via a degenerated Andronov--Hopf type bifurcation, adding at the very end the sliding effects. Finally, we use the Poincare'\--Miranda theorem for obtaining an explicit piecewise linear holomorphic system with 3 limit cycles, a result that improves the known examples in the literature that had a single limit cycle. (AU) | |
| FAPESP's process: | 20/06708-9 - Piecewise Holomorphic Systems and Regularization of Filippov fields around degenerated singularities and regular tangential polycycles |
| Grantee: | Gabriel Alexis Rondón Vielma |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 22/12123-9 - Piecewise holomorphic systems and regularization of Filippov systems |
| Grantee: | Gabriel Alexis Rondón Vielma |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| FAPESP's process: | 23/02959-5 - Non-Smooth Systems and Singular Perturbations |
| Grantee: | Paulo Ricardo da Silva |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |