Dynamical Systems: Maps and Stability

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Explores the Kuramoto model for synchronization in phase oscillators and discusses stability criteria and critical coupling values.

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Covers Hopf bifurcations, pitchfork bifurcations, and the Lorenz system in nonlinear dynamics and chaos.

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Delves into homoclinic orbits, bifurcations, and limit cycles in nonlinear dynamics.

Explores Chaos Theory, focusing on the logistic map, periodic orbits, and stability conditions.

Delves into Chaos Theory, exploring chaotic systems, sensitivity to initial conditions, and the dynamics of the double pendulum.

Covers the formalism and bases of dynamic systems, including differential equations and non-linear systems.

Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.