Bifurcation Theory

Abstract

Bifurcation theory is concerned with the question of how the behavior of a system which depends on a parameter p changes with the parameter. It focuses on any critical value, p = p _cr , where the behavior of the system undergoes radical change; such values are called bifurcation points. Consider for example the case of a cell which grows and replicates. During the cell cycle, there occur several critical times when the cell moves from one phase to another. The first such time occurs at the check point R ₁ when the cell commits to begin replicating its DNA . The biological process about R ₁ can be described by a network of signaling proteins whose dynamics is triggered by a cyclin-dependent kinase, Cdk. When the concentration p of this kinase exceeds some critical level p _cr , the protein network allows the cell to pass the check point R ₁ and to start replicating its DNA.