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Description: Attractors and invariant measures for nonlinear dynamical systems. Measures of chaos like Lyapunov exponents. Time series analysis. Parametric excitation. Multiple time scales and singular perturbation theory. Dynamics and synchronization of coupled neuronal oscillators. Nonlinear dynamics in cellular and molecular biology. Analytical dynamics of mechanical systems and modal analysis, including methods for high modal density limits. Strong emphasis on applications to realistic biological and mechanical systems.