  Bursting oscillations are commonly seen as a mechanism for information coding
in neuroscience and have also been observed in many physical, biochemical, and
chemical systems. This study focuses on the computational investigation of
mixed-mode bursting oscillations (MMBOs) generated by a simple two-dimensional
integrate-and-fire-or-burst (IFB) model. We demonstrate a new paradigm for the
generation of MMBOs, where birhythmicity and noise are the key components. In
the absence of noise, the proposed model exhibits birhythmicity of two
independent bursting patterns, bursts of two spikes and bursts of three spikes,
depending on the initial condition of the model. Noise induces the random
transitions between two bursting states which leads to MMBOs, and the
transition rate increases with the noise intensity. Our results provide a
systematic view of the roles of noise and initial condition: the bursting
dynamics produced by the proposed model heavily rely on the initial conditions
when noise is weak; while for intermediate and strong noise, the burst dynamics
are independent of the initial condition.
