Course

PHYS-460: Nonlinear dynamics, chaos and complex systems

Lectures in this course (15)

Covers chaotic behavior in complex systems, with applications in various fields and a historical overview of major developments in chaos theory.

Covers key concepts in nonlinear dynamical systems, such as existence, uniqueness, and continuous dependence of solutions.

Introduces equilibrium points and bifurcations in differential equations, discussing their stability and relevance in various contexts.

Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.

Explores fixed point stability, Lyapunov functions, Lotka-Volterra models, and nonlinear dynamics in complex systems.

Covers special types of systems, focusing on gradient systems and limit cycles, discussing equilibrium points, stability, and chaotic behavior.

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

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

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

Covers bifurcations, long-term dynamics, logistic map, universality, and correspondence between different maps.

Explores logistic maps, bifurcations, equilibrium points, and periodic orbits in nonlinear dynamics and chaos.

Delves into renormalization, fractals, and strange attractors, exploring the properties of countable and uncountable sets.

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

Delves into complex systems, strange attractors, and epidemics, emphasizing the influence of psychological factors and the role of contagion.

Covers classical models of epidemic spreading and dynamics on networks with examples.