This book will present a comprehensive exploration of the geometric theory ofnbsp;bifurcations (GBT), a novel approach that employs information geometry to analyzenbsp;dynamical systems. It will delve into the mathematical foundations of GBT, including thenbsp;Riemannian metrical structure of parameter spaces, Fisher information metric, scalarnbsp;curvature, and their application to local and global bifurcations. The book will cover thenbsp;limitations of classical bifurcation theory (CBT) and demonstrate how GBT overcomesnbsp;these by providing a more complete characterization of stability and addressing thenbsp;global behavior of nonlinear dynamical systems. Specific topics will include thenbsp;geometric interpretation of bifurcations, stability analysis using curvature scalar, scalingnbsp;analysis using Fisher information, and the application of GBT to study complex andnbsp;nonlinear phenomena, especially where the standard methods show little or no solution.
