  We study the phenomenological model of ensemble of two FitzHugh-Nagumo
neuron-like elements with symmetric excitatory couplings. The main advantage of
proposed model is the new approach to model of coupling which is implemented by
smooth function that approximate rectangular function. The proposed coupling
depends on three parameters that define the beginning of activation of an
element $\alpha$, the duration of the activation $\delta$ and the strength of
the coupling $g$. We observed a rich diversity of types of neuron-like
activity, including regular in-phase, anti-phase and sequential spiking
activities. In the phase space of the system, these regular regimes correspond
to specific asymptotically stable periodic motions (limit cycles). We also
observed a chaotic anti-phase activity, which corresponds to a strange
attractor that appears due to the cascade of period doubling bifurcations of
limit cycles.
  We also provide the detailed study of bifurcations which lead to transitions
between all these regimes and detect on the $(\alpha, \delta)$ parameter plane
those regions that correspond to the above-mentioned regimes. We also show
numerically the existence of bistability regions when various non-trivial
regimes coexist. For example, in some regions, one can observe either
anti-phase or in-phase oscillations depending on initial conditions. We also
specify regions corresponding to coexisting various types of sequential
activity.
