We describe all heteroclinic networks in R4 made of simple heteroclinic cycles of types B or C, with at least one common connecting trajectory. For networks made of cycles of type B, we study the stability of the cycles that make up the network as well as the stability of the network. We show that even when none of the cycles has strong stability properties, the network as a whole may be quite stable. We prove, and provide illustrative examples of, the fact that the stability of the network does not depend a priori uniquely on the stability of the individual cycles.
We describe all heteroclinic networks in R4 made of simple heteroclinic cycles of types B or C, with at least one common connecting trajectory. For networks made of cycles of type B, we study the stability of the cycles that make up the network as well as the stability of the network. We show that even when none of the cycles has strong stability properties, the network as a whole may be quite stable. We prove, and provide illustrative examples of, the fact that the stability of the network does not depend a priori uniquely on the stability of the individual cycles.