Artículos de revistas
Transcritical and zero-Hopf bifurcations in the Genesio system
Fecha
2017-04-01Registro en:
Nonlinear Dynamics, v. 88, n. 1, p. 547-553, 2017.
1573-269X
0924-090X
10.1007/s11071-016-3259-2
2-s2.0-85007492396
2-s2.0-85007492396.pdf
8032879915906661
0000-0002-8723-8200
Autor
Universidade Estadual Paulista (Unesp)
Universitat Autònoma de Barcelona
Institución
Resumen
In this paper we study the existence of transcritical and zero-Hopf bifurcations of the third-order ordinary differential equation x⃛ + ax¨ + bx˙ + cx- x2= 0 , called the Genesio equation, which has a unique quadratic nonlinear term and three real parameters. More precisely, writing this differential equation as a first-order differential system in R3 we prove: first that the system exhibits a transcritical bifurcation at the equilibrium point located at the origin of coordinates when c= 0 and the parameters (a, b) are in the set { (a, b) ∈ R2: b≠ 0 } \ { (0 , b) ∈ R2: b> 0 } , and second that the system has a zero-Hopf bifurcation also at the equilibrium point located at the origin when a= c= 0 and b> 0.