Transcritical Bifurcation: Theory and Applications

This lecture delves into the theory and applications of transcritical bifurcation, explaining the change of coordinates to simplify the Taylor expansion of F(x,μ). The slides cover the mathematical details of the transcritical bifurcation, including the critical points and stability analysis. The lecture also discusses the local stability of the system and provides insights into isolated bifurcations. Key concepts such as the Jacobian matrix and eigenvalues are explored in the context of dynamical system theory.