Heteroclinic networks in an ensemble of generalized Lotka–Volterra elements

In this article, the generalized four-dimensional Lotka–Volterra model is studied. The model consists of four units coupled with excitatory or inhibitory couplings. It is shown that in the phase space of the model, there exists a heteroclinic network—a connected union of two or more heteroclinic cycles (see definition in the text). A partition of the plane of coupling’s parameters into regions of the existence of various heteroclinic networks is constructed. The presence of a stable heteroclinic cycle in the phase space of neuronal models, including the model under consideration, can be considered as the implementation of the process of switching neuronal activity. It is shown that the system under study can exhibit multistability.