On the dynamics of a Van der Pol–Duffing snap system - Wiggers V.* (2022)
© 2022, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.Abstract: In this paper, we propose an autonomous snap oscillator which was obtained from the Van der Pol–Duffing forced oscillator. The proposed system presents polynomial nonlinearities, being modeled by a four-parameter fourth-order ordinary differential equation. We investigate the dynamics of this system. More specifically, keeping two of the parameters fixed, we investigate numerically the organization of chaos and periodicity in this system, using an appropriately chosen parameter plane. We show that such parameter plane presents parameters regions for which the multistability phenomenon is perfectly characterized. Plots of basins of attraction and coexisting attractors are presented. An analytical investigation regarding the stability of equilibrium points was also carried out. Graphic abstract: [Figure not available: see fulltext.]