Mixed-mode oscillations and chaos from a simple second-order oscillator under weak periodic perturbation

In this study, we propose a remarkably simple oscillator that exhibits extremely complicated behaviors. The second-order nonautonomous differential equation discussed in this Letter is considered to be one of the simplest dynamics that can produce mixed-mode oscillations (MMOs) and chaos. Our model uses a Bonhoeffer–van der Pol (BVP) oscillator under weak periodic perturbation. The parameter set of the BVP equation is chosen such that a focus and a relaxation oscillation coexist when no perturbation is applied. Under weak periodic perturbation, various types of MMOs and chaos with remarkably complicated waveforms are observed.

► We propose a remarkably simple oscillator exhibiting extremely complicated behaviors.
► The oscillator can produce mixed-mode oscillations (MMOs) and chaos.
► Our model uses a BVP oscillator under weak periodic perturbation.
► The parameter set is chosen so that two solutions coexist without perturbation.
► Under weak periodic perturbation, various types of MMOs and chaos are observed.