Bifurcation and Stability in Nonlinear Dynamical Systems

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The book introduces a comprehensive theory for analyzing bifurcation and stability in nonlinear dynamical systems, particularly focusing on higher-order singularity equilibriums. It addresses the complexities of infinite-equilibrium systems, which exhibit unique dynamical behaviors akin to discontinuous systems. Key concepts such as stability on specific eigenvectors, spiral stability, and Hopf bifurcation are explored using Fourier series transformation. By examining (2m)th and (2m+1)th-degree polynomial systems, it offers insights into the dynamics of infinite-equilibrium systems, paving the way for advancements in dynamical systems and control.