This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums
in nonlinear dynamical systems. Until now, one does not have any efficient way to investigate stability and bifurcation of
dynamical systems with higher-order singularity equilibriums. For instance, infinite-equilibrium dynamical systems have higher-order
singularity, which dramatically changes dynamical behaviors and possesses the similar characteristics of discontinuous dynamical
systems. The stability and bifurcation of equilibriums on the specific eigenvector are presented, and the spiral stability
and Hopf bifurcation of equilibriums in nonlinear systems are presented through the Fourier series transformation. The bifurcation
and stability of higher-order singularity equilibriums are presented through the (2m)th and (2m+1)th -degree polynomial systems.
From local analysis, dynamics of infinite-equilibrium systems is discussed. The research on infinite-equilibrium systems will
bring us to the new era of dynamical systems and control.
Presents an efficient way to investigate stability
and bifurcation of dynamical systems with higher-order singularity equilibriums;
Discusses dynamics of infinite-equilibrium
Demonstrates higher-order singularity.