Periodic Solutions and Bifurcations in a Long-Timescale Oceanic Carbon Cycle Model

We study the dynamics of a recent model of Rothman for long timescale carbon cycle. We reproduce and extend variousresults of the Rothman model. We present numerical results showing that the model exhibits both stable and unstable limitcycles via Hopf bifurcations as the parameters are varied. We numerically find normal forms of Bautin bifurcations to confirmtheir criticality. We also extend the analysis of the normal form coefficients to identify where the fold limit cycle bifurcationoccurs.