The Geometric Bifurcation Theory
摘要
In this chapter, we present the notation and the relevant theoretical background, consisting of a detailed exposition of the mathematical framework of Geometric Bifurcation Theory. This includes the construction of Riemannian manifolds from dynamical systems, the Fisher information metric, and the role of scalar curvature in detecting bifurcations, local structural stability, and the character of phase–space trajectories. There is no need of any prior knowledge of information or differential geometry.