https://doi.org/10.1140/epjp/s13360-022-02498-w
Regular Article
Complex mixed-mode oscillations in oscillators sharing nonlinearity
1
Department of Physics, Central University of Rajasthan, 305 817, Ajmer, India
2
Center for Nonlinear Systems, Chennai Institute of Technology, 600 069, Chennai, Tamil Nadu, India
3
Department of Nonlinear Dynamics, Bharathidasan University, 620024, Tiruchirappalli, Tamil Nadu, India
Received:
7
January
2022
Accepted:
16
February
2022
Published online:
28
February
2022
Mixed-mode oscillations (MMOs) are a typical manifestation of slow-fast dynamical systems that contains a sequence of large amplitude excursions interspersed with small amplitude oscillations. We identified complex forms of MMOs in a system of three coupled non-autonomous LCR oscillators sharing a common nonlinearity. Different sequences of MMOs and related dynamics like MMO incrementing bifurcations, Farey sequences, and amplitude-modulated spiking have been witnessed in the model as a consequence of 2-slow and 1-fast external driving frequencies. For particular parametric space, the period adding sequence of MMOs is found to follow a devil’s staircase structure. The transition between states is found to occur via torus canards explosion. We validate our observations through numerical investigation.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
