Natural cycles and pollution

In the short run, the two steady states can collide and disappear through a saddle-node bifurcation. Since consumption and natural resource are substitutable goods, a limit cycle can arise around the higher stationary state. To the contrary, this kind of cycles never occurs around the lower steady state, no matter the resource effect on consumption. Finally, focusing on the variety of bifurcations of codimension two, we find a Bogdanov-Takens loop.