On the bifurcation of species

We propose and analyze a model of evolution of species based upon a general description of phenotypes in terms of a single quantifiable characteristic. In the model, species spontaneously arise as solitary waves whose members almost never mate with those in other species, according to the rules laid down. The solitary waves in the model bifurcate and we interpret such events as speciation. Our aim in this work is to determine whether a generic mathematical mechanism may be identified with this process of speciation. Indeed, there is such a process in our model: it is the Andronov homoclinic bifurcation. It is robust and is at the heart of the formation of new solitary waves, and thus (in our model) new species.