Modeling and analysis of complex nonlinear dynamical systems.
Introduction of fundamental mathematical concepts for understanding and analyzing autonomous linear and non linear ordinary differential equations, including qualitative analysis.
Criteria and theorems for the asymptotic stability of equilibria.
Linearization and Hartman-Grobman theorem.
Linear and nonlinear oscillations (limit cycles).
Bifurcations: saddle-node, transcritical, pitchfork and Hopf bifurcations in continuous time, flip and period doubling bifurcations in discrete and continuous time, respectively.
Bifurcation cascades and routes to chaos.
Chaotic attractors and fractals.
Simulation of nonlinear systems. Software tools for the analysis of complex systems: MATLAB.
Analysis and simulation of complex systems in multidisciplinary fields: physical, biological, ecological and economic systems.