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Time evolution of a mean-field generalized contact process

We investigate the macroscopic time evolution and stationary states of a mean field generalized contact process in $\mathbb{R}^d$. The model is described by a coupled set of nonlinear integral-differential equations. It was inspired by a model of neurons with discrete voltages evolving by a stochastic integrate and fire mechanism. We obtain a complete solution in the spatially uniform case and partial solutions in the general case. The system has one or more fixed points and also traveling wave solutions.