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This paper addresses neural architectures based on coupled nodes that exhibit chaotic dynamics, and it establishes the relationship between these networks and bifurcating spiking model neurons based on the integrate and fire model neuron. The nodes of the studied networks are mathematically described through recursive maps, also named recursive processing elements - RPEs, which interact through parametric coupling, i.e., through dynamic modulation of the bifurcation parameters. We have the definition of two macro states that are exercised by the RPEs networks during operation: (a) stable spatio-temporal collective patterns, and (b) high complexity dynamical activity for the search in the state space. The relationship between these macro states and the configurations of assemblies of spiking model neurons is established, as well as the mechanisms of sustainability and dissolution of these macro states are discussed.