Bifurcation Theory - Saddle-Node, Hopf, Transcritical, Pitchfork
Explore saddle-node, transcritical, pitchfork, and Hopf bifurcations in dynamical systems. Learn how these phenomena affect phase portraits and system behavior as parameters change.
Underactuated Robotics - Spring 2009
This course discusses nonlinear dynamics and control of underactuated mechanical systems, with an emphasis on machine learning methods.
Topics in Nonlinear Dynamics
Explore nonlinear dynamics through critical points, Hamiltonian systems, bifurcations, limit cycles, discrete-time dynamics, and stochastic processes. Gain insights into complex system behaviors and analysis techniques.
Topics in Nonlinear Dynamics
This is a basic course in classical mechanics at the senior undergraduate/ master's level. It covers the standard topics in this subject, including the Lagrangian and Hamiltonian formalisms. It also places the subject in the broader context of classical…
Nonlinear Dynamics and Chaos
Explore nonlinear dynamics and chaos through analytical methods, examples, and applications in physics, biology, and engineering. Develop mathematical theory and gain insights into complex systems behavior.
Exponentials, Economics, and Ecology with David Krakauer
Explore exponential changes, nonlinear dynamics, and interconnected systems in ecology and economics. Gain insights on aligning individual and public good in a complex world.
Loss of Self-Organization in Earth's Climate
Análisis de cambios en la autorregulación del clima terrestre mediante herramientas de sistemas complejos, comparando datos de temperatura global con el modelo Daisyworld.
The Thermodynamics of Communication - Exploring Energy and Information Limits
Exploring the fundamental relationship between energy, information, and matter in communication processes. Discusses nonlinear dynamics of communication channels and their implications for collective intelligence and limits to human knowledge.
Nonlinear Dynamics of Beliefs over Social Networks
Explore how social networks, internal biases, and belief systems shape group dynamics and decision-making in complex social environments.
What is Lyfe? Towards a Biology of Context and Complexity
Exploring a multidimensional view of biology beyond genomics, emphasizing history, context, environment, and narrative to reframe our understanding of life and its complexities.
How Is the Landscape Upon Which Life Evolves Selected - Spontaneous Emergence of Modularity
Explore the emergence of modularity in biology, its impact on evolution, and connections to environmental variability through advanced physics concepts and experimental insights.
Computing with Dynamical Systems - From Implementations Towards Novel Concepts
Explore dynamical systems in computing, from practical implementations to cutting-edge concepts. Gain insights into complex systems and interdisciplinary physics applications.
Nonlinear Dynamics of Active Solids Through Nonreciprocal Mechanochemical Feedback
Explore nonlinear dynamics of active solids through nonreciprocal mechanochemical feedback. Gain insights into collective phenomena in energy-consuming systems and their applications in various fields.
Generalization in Robotic Behavior Cloning: Pitfalls and Promises
Explore challenges and solutions in robotic behavior cloning, focusing on generalization in continuous state/action spaces. Gain insights into frameworks enabling agents to imitate complex behaviors with provable guarantees.
Dynamical Complexity in the Rössler System
Uncover the analytical connection between Rössler equations and the logistic family. Explore periodic orbits, topologies, and complex dynamics in this mathematical exploration of chaotic attractors.
Sparse Nonlinear Dynamics Models with SINDy - The Library of Candidate Nonlinearities
Explores advanced techniques for SINDy algorithm, including control variables, bifurcation parameters, rational functions, dimensionality reduction, and symmetry constraints in nonlinear dynamics modeling.
Normal Forms for Vector Fields
Introduction to normal forms for vector fields, focusing on simplifying nonlinear terms and determining topological equivalence. Covers theory, examples, and applications in dynamical systems analysis.
Center Manifolds for Hamiltonian Systems and PDEs - Lorenz System Bifurcation, Part 2
Explore center manifolds in Hamiltonian systems and PDEs, including Lorenz system bifurcation, unstable directions, and applications to flame front evolution and celestial mechanics.
Center Manifold Theory - Computing Center Manifolds
Explore center manifold theory for dynamical systems, focusing on computing and approximating center manifolds. Learn to analyze stability and dynamics near equilibrium points using Taylor series expansions and tangency conditions.
Stability of Periodic Orbits - Floquet Theory - Stable and Unstable Invariant Manifolds
Explore stability of periodic orbits using Floquet theory. Learn about monodromy matrices, Floquet multipliers, and invariant manifolds in Hamiltonian systems. Understand the foundations of chaos in dynamical systems.
Periodic Systems and Periodic Motion - Parametric Resonance Tongues of Instability, Mathieu Equation
Explore periodic systems, parametric resonance, and the Mathieu equation. Learn about resonance tongues, stability analysis, and the fascinating Kapitza pendulum phenomenon in nonlinear dynamics.