Alternative Stable States, Coral Reefs, and Smooth Dynamics with a Kick.

We consider a computer simulation, which was found to be faithful to time series data for Caribbean coral reefs, and an analytical model to help understand the dynamics of the simulation. The analytical model is a system of ordinary differential equations (ODE), and the authors claim this model demonstrates the existence of alternative stable states. The existence of an alternative stable state should consider a sudden shift in coral and macroalgae populations, while the grazing rate remains constant.

Dynamic stabilization in the PU1-GATA1 circuit using a model with time-dependent kinetic change.

The PU.1 and GATA1 genes play an important role in the differentiation of blood stem cells. The protein levels expressed by these genes are thought to be regulated by a self-excitatory feedback loop for each gene and a cross-inhibitory feedback loop between the two genes.