In this paper, we use concepts and results from percolation theory to investigate and characterize the effects of multi-channels on the connectivity of Dynamic Spectrum Access networks. In particular, we focus on the scenario where the secondary nodes have plenty of vacant channels to choose from-a phenomenon which we define as channel abundance. To cope with the existence of multi-channels, we use two types of rendezvous protocols: naive ones which do not guarantee a common channel and advanced ones which do. We show that, with more channel abundance, even with the use of either type of rendezvous protocol, it becomes difficult for two nodes to agree on a common channel, thereby potentially remaining invisible to each other. We model this invisibility as a Poisson thinning process and show that invisibility is even more pronounced with channel abundance. Following the disk graph model, we define and characterize connectivity of the secondary network in terms of the available number of channels, deployment densities, number of transceivers per node, and communication range. When primary users are absent, we derive the critical number of channels which maintains super-criticality of the secondary network. When primary users are present, we characterize and analyze the connectivity for all the regions: channel abundance, optimal, and channel deprivation. Our results can be used to decide on the goodness of any channel rendezvous algorithm by computing the expected resultant connectivity.
