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This course introduces bifurcations in two-dimensional systems, exploring the creation, destruction, and destabilization of fixed points and closed orbits as parameters vary. The course covers saddle-node, pitchfork bifurcations, and provides examples from genetic regulatory systems. The learning outcomes include understanding bifurcations in 2D systems, birth of periodic orbits via Hopf bifurcation, and classifying fixed points. The course teaches skills such as analyzing nullclines, center manifold theory, and gradient systems. The teaching method includes lectures, examples, and references to additional resources. The intended audience for this course includes students and professionals interested in nonlinear dynamics, bifurcation theory, and dynamical systems.
