Uniform isochronous centers in planar polynomial differential systems of degree 5
Periodic solutions dor discontinuous dynamical systems with symmetry
Non-smooth dynamical systems: qualitative theory and structural stability
| Full text | |
| Author(s): |
Itikawa, Jackson
;
Llibre, Jaume
;
Mereu, Ana Cristina
;
Oliveira, Regilene
Total Authors: 4
|
| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 22, n. 9, p. 3259-3272, NOV 2017. |
| Web of Science Citations: | 1 |
| Abstract | |
We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems <(x) over dot> = -y + x(2)y; <(y) over dot> = x + xy and <(x) over dot> = -y + x(2) y; <(y) over dot = x + xy(2), when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. Using averaging theory of first order the maximum number of limit cycles that we can obtain is twice the maximum number of limit cycles obtained in a previous work for discontinuous quadratic differential systems perturbing the same uniform isochronous quadratic center at origin perturbed with two zones separately by a straight line, and 5 more limit cycles than those achieved in a prior result for discontinuous cubic differential systems with the same uniform isochronous cubic center at the origin perturbed with two zones separately by a straight line. Comparing our results with those obtained perturbing the mentioned centers by the continuous quadratic and cubic differential systems we obtain 8 and 9 more limit cycles respectively. (AU) | |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support type: | Research Projects - Thematic Grants |
| FAPESP's process: | 14/00304-2 - Singularities of differentiable mappings: theory and applications |
| Grantee: | Maria Aparecida Soares Ruas |
| Support type: | Research Projects - Thematic Grants |
| FAPESP's process: | 15/07612-7 - Uniform isochronous centers in planar polynomial differential systems of degree 5 |
| Grantee: | Jackson Itikawa |
| Support type: | Scholarships in Brazil - Post-Doctorate |