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Geometric Bifurcation Theory
Fisher Information Geometry Applied to Dynamic and Complex Systems
Introduction to Geometric Bifurcation Theory
This book will present a comprehensive exploration of the geometric bifurcation theory (GBT), a novel approach that employs information geometry to analyze dynamical systems.
Mathematical Foundations of GBT
It will delve into the mathematical foundations of GBT, including the Riemannian metrical structure of parameter spaces, Fisher information metric, scalar curvature, and their application to local and global bifurcations.
Limitations of Classical Bifurcation Theory
The book will cover the limitations of classical bifurcation theory (CBT) and demonstrate how GBT overcomes these by providing a more complete characterization of stability and addressing the global behavior of nonlinear dynamical systems.
Topics Covered
Specific topics will include the geometric interpretation of bifurcations, stability analysis using curvature scalar, scaling analysis using Fisher information, and the application of GBT to study complex and nonlinear phenomena, especially where the standard methods show little or no solution.
