Dynamical behaviour of a polynomial two dimensional nonlinear oscillator
speaker: Angelo Di Garbo (CNR Pisa)abstract: Diego Febbe 1 , Riccardo Mannella 2 , Riccardo Meucci 3 , Angelo Di Garbo 2,4
1 Physics Department, University of Pisa, Pisa, Italy 2 Institute of Biophysics, CNR-National Research Council, Pisa, Italy 3 Physics and Astronomy Department, University of Firenze, Sesto Fiorentino, Firenze, Italy 4 National Institute of Optics, CNR-INO, Firenze, Italy.
In the qualitative theory of ordinary differential equations the study of limit cycles is an important topic having several implications both in the theory of dynamical systems and applications 1-4. In our contribution a specific planar dynamical system of polynomial type was investigated 5. This nonlinear oscillator can be used to describe self-sustained oscillations of some nonlinear circuits. It was shown that this planar dynamical system exhibits several dynamical regimes: stationary states, limit cycles and bistability. Chaotic dynamics can occur when an harmonic periodic perturbation is applied. Moreover it was shown that synchronisation phenomena can occur when these planar dynamical systems are coupled diffusively.
1 Freddy Dumortier , Jaume Llibre , Joan C. Artés. Qualitative Theory of Planar Differential Systems. Springer Universitext, 2006. 2 Yan-Qian Ye. Theory of Limit Cycles. American Mathematical Society, Translations of mathematical monographs, vol. 66, 1986. 3 Aleksandr A. Andronov, Aleksandr A. Vitt, Semen E. Khaikin. Theory of Oscillators: Adiwes International Series in Physics (Vol. 4). Elsevier, 2013. 4 Albert C. J. Luo. Limit cycles and homoclinic networks in two-dimensional polynomial systems. Chaos, 34, 022104, 2024. 5 Diego Febbe, Riccardo Mannella, Riccardo Meucci, Angelo Di Garbo. Dynamical behaviour of a new model for the UJT relaxation oscillator. Chaos, Solitons and Fractals, 183, 114906, 2024.
timetable:
Thu 12 Sep, 11:30 - 12:05, Aula Dini
documents:
ABSTRACT
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