Neural nets are generally considered to be connected synaptically. However, the majority of information transfer in the brain may not be by synapses. Nonsynaptic diffusion neurotransmission (NDN) may be a major mechanism for information transfer in the brain. In this paper, a model of a diffusive-only neural net, based on a ligand-receptor dynamics, is presented. A mechanism of active release of neurotransmitters as a response to binding, along with one of depletion of free ligands, make the net capable of spontaneous activity. States of thermodyamical equilibrium, and trajectory of the system in the phase space have been numerically determined. The results indicate the possibility of chaotic behavior. The relevance of the theoretical model to the study of some brain mass-sustained functions is discussed.