Buffer phenomenon in neurodynamics (Q1761005)

The authors consider a singularly perturbed scalar nonlinear differential-delay equation with two delays modeling the electrical activity of a neuron. This equation is of the type \[ \varepsilon{du\over dt}= u[(a+ 1) f(u(t-\varepsilon h))- a- by(u(t- 1))], \] where \(a\), \(b\), \(h\) are positive parameters, \(0<\varepsilon\ll 1\). They formulate conditions on the functions \(f\) and \(g\) such that \((*)\), for sufficiently small \(\varepsilon\), has any prescribed finite number of stable periodic solutions. This property is called buffer phenomenon.