(untitled) (European Journal of Pure and Applied Mathematics, 2024)
We study the dynamics of a recent model of Rothman for long timescale carbon cycle. We reproduce and extend various results of the Rothman model. We present numerical results showing that the model exhibits both stable and unstable limit cycles via Hopf bifurcations as the parameters are varied. We numerically find normal forms of Bautin bifurcations to confirm their criticality. We also extend the analysis of the normal form coefficients to identify where the fold limit cycle bifurcation occurs.