Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional oscillations exhibit a finite number of damped oscillations...

Real neurons can exhibit various types of firings including tonic spiking, bursting as well as silent state, which are frequently observed in neuronal electrophysiological experiments. More interestingly, it is found that neurons can demonstrate the co-existing mode of stable tonic spiking and...

We present a simple two-dimensional dynamical system where two nonlinear terms, exerting respectively positive feedback and reversal, compete to create a singularity in finite time decorated by accelerating oscillations. The power law singularity results from the increasing growth rate. The...