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For scalar reaction-diffusion equations, a traveling wave is a front whichtransforms a higher energy state to a lower energy state. The same is true fora system of equations with a gradient structure. At the core of thisphenomenon, the wave propagation results in an invasion of an equilibrium statefrom a different one. This paper is aimed at two questions:  (i) Can reaction-diffusion waves exhibit front propagation in both directionsbetween two distinct equilibrium states? (ii) The co-existence of travelingfronts and pulses; a subject rarely studied.  Working on a FitzHugh-Nagumo model with the same physical parameters, we givepositive answers to both questions.

Front propagation in both directions and coexistence of traveling fronts and pulses