We are interested in the question of how jealousy influences the dynamics of populations. In a previous paper, we investigated the impact of power and jealousy on cooperation. By using intelligent agents, a stochastic updating process has been used, so that artificial agent populations could be modelled. In this paper, we investigate update procedures based on deterministic dynamics for populations arranged in a lattice. Compared to stochastic processes, our findings show that populations behave and react far more dynamically, in certain parameter regions, when spatial cooperation is applied.