Speciation is the splitting of a single species into two species and qualifies as a bifurcation phenomenon. Has bifurcation theory ever been applied to speciation? If so, how? Any published references?
I don't have access to it, but is this the sort of stuff you're looking for?
Volkenstein, M.V. and Livshits, M.A., 1989. Speciation and bifurcations. BioSystems, 23(1), pp.1-5.
Abstract
The interrelations of physics and biology are discussed. It is shown that Darwin can be considered as one of the founders of the important field of contemporary physics called physics of dissipative structures or synergetics. The theories of gradual and punctual evolution are presented. The contradiction between these theories can be solved on the basis of molecular theory of evolution and on the basis of the phenomenological physical treatment. The general physical properties of living systems, considered as open systems being far from equilibrium, are listed and simple non-linear mathematical models describing gradual and punctual speciation are suggested. The usual pictures which present these two kinds of speciation can possess physico-mathematical sense. Punctuated speciation means bifurcation, a kind of non-equilibrium phase transition.