A delayed biophysical system for the Earth's climate

We consider further the Differential Daisyworld model of Watson and Lovelock that we have analyzed in a previous paper (De Gregorio et al., 1992). In this work we introduce a delay in the birthrate of the species. We consider three different models: the constant time lag model and the strong and the weak delay models. In the weak delay case no value of the delay changes the asymptotic stability of the stationary solutions. In the constant time lag and in the strong delay models, however, there exists a critical value of the delay, above which periodic solutions appear. These periodic solutions are numerically found to be globally attracting even for large delay when the linear approximation analysis is no longer valid. For both models, very regular behavior is obtained if the percentage coverage of the fertile ground of the Earth is much less than 1. As the percentage of the fertile ground increases, however, chaotic behavior is possible.