On the number of spikes of solutions for a forced singularly perturbed differential equation (Q2504894)

The paper deals with the perturbed system \(\frac{dv}{dt}=a\sin (\upsilon t)-i,\) \(\varepsilon \frac{di}{dt}=v-\phi (i)\) where \(v,i\) are the voltage and current, respectively, \(\varepsilon >0\) is a small parameter, \(\phi \) is piecewise linear and S-shaped. The fundamental property of the above system is the relaxation oscillation of its solutions. The authors present a detailed study of the spiking phenomena over a fixed finite time interval, in particular, the number of spikes over a finite time interval and their bifurcation.