| Full text | |
| Author(s): |
Messias, Marcelo
;
Reinol, Alisson C.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | NONLINEAR DYNAMICS OF STRUCTURES, SYSTEMS AND DEVICES, VOL I, NODYCON 2019; v. N/A, p. 9-pg., 2020-01-01. |
| Abstract | |
From the normal form of polynomial differential systems in R3 having a sphere as invariant algebraic surface, we obtain a class of quadratic systems depending on ten real parameters, which encompasses the well-known Sprott A system. For this reason, we call them generalized Sprott A systems. In this paper, we study the dynamics and bifurcations of these systems as the parameters are varied. We prove that, for certain parameter values, the z-axis is a line of equilibria, the origin is a non-isolated zero-Hopf equilibrium point, and the phase space is foliated by concentric invariant spheres. By using the averaging theory we prove that a small linearly stable periodic orbit bifurcates from the zero-Hopf equilibrium point at the origin. Finally, we numerically show the existence of nested invariant tori around the bifurcating periodic orbit. (AU) | |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |