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In this paper we introduce a dynamical model for wireless sensor networks. We obtain a convergent martingale for the broadcast process in such networks. To our knowledge, such martingales were unknown previously. We look at a formal model using the formalisms of martingales, dynamical systems and Markov chains, each formalism providing complementary and coherent information with each other. The model is partly validated with numerical simulation of wireless sensor networks, we informally make explicit the situations where the model is realistic. We also provide an alternative dynamical model based on the hypothesis that the distribution of the location of the emitting sensors is uniform. This hypothesis is more fulfilled when the emission radius r becomes larger and emission angle α smaller. In the situations where the hypothesis is close to be fulfilled good agreements between numerical …