  Complex network dynamics have been analyzed with models of systems of coupled
switches or systems of coupled oscillators. However, many complex systems are
composed of components with diverse dynamics whose interactions drive the
system's evolution. We, therefore, introduce a new modeling framework that
describes the dynamics of networks composed of both oscillators and switches.
Both oscillator synchronization and switch stability are preserved in these
heterogeneous, coupled networks. Furthermore, this model recapitulates the
qualitative dynamics for the yeast cell cycle consistent with the hypothesized
dynamics resulting from decomposition of the regulatory network into dynamic
motifs. Introducing feedback into the cell-cycle network induces qualitative
dynamics analogous to limitless replicative potential that is a hallmark of
cancer. As a result, the proposed model of switch and oscillator coupling
provides the ability to incorporate mechanisms that underlie the synchronized
stimulus response ubiquitous in biochemical systems.
