Courses

Autonomous two-dimensional SDE systems, equilibrium points and their stability, the importance of nonlinearity. Population systems with competitive Lotka-Volterra relations and other applications. Hamiltonian systems, derived systems. Local and non-local stability, Lyapunov functions. Periodic solutions, limit cycles and the Poincaré-Bendixson theorem. The Van der Pol oscillator and other applications. The concept of structural stability/instability. Bifurcations of fixed points and periodic trajectories: sagittal-node bifurcation, postcritical bifurcation, fork bifurcation and Hopf bifurcation. SDE systems of three or more dimensions, the emergence of chaotic behavior, the Lorenz attractor and other chaotic ("strange") attractors.