Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nose-Hoover Oscillator

Author(s)

Llibre, Jaume ^[1] ; Messias, Marcelo ^[2] ; Reinol, Alisson C. ^{[3, 4]}

Affiliation

^[1] Univ Autonoma Barcelona UAB, Dept Matemat, Bellaterra 08193, Barcelona Ct - Spain

^[2] Univ Estadual Paulista UNESP, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP - Brazil

^[3] Univ Tecnol Fed Parana, Dept Acad Matemat, UTFPR, BR-86812460 Apucarana, Parana, Brazil.Llibre, Jaume, Univ Autonoma Barcelona UAB, Dept Matemat, Bellaterra 08193, Barcelona Ct - Spain

^[4] Univ Tecnol Fed Parana, Dept Acad Matemat, UTFPR, BR-86812460 Apucarana, Parana - Brazil

• Document type: Journal article
• Source: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS; v. 27, n. 3 JUN 2020.
• Web of Science Citations: 0

Abstract

We perform a global dynamical analysis of a modified Nose-Hoover oscillator, obtained as the perturbation of an integrable differential system. Using this new approach for studying such an oscillator, in the integrable cases, we give a complete description of the solutions in the phase space, including the dynamics at infinity via the Poincare compactification. Then using the averaging theory, we prove analytically the existence of a linearly stable periodic orbit which bifurcates from one of the infinite periodic orbits which exist in the integrable cases. Moreover, by a detailed numerical study, we show the existence of nested invariant tori around the bifurcating periodic orbit. Finally, starting with the integrable cases and increasing the parameter values, we show that chaotic dynamics may occur, due to the break of such an invariant tori, leading to the creation of chaotic seas surrounding regular regions in the phase space. (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