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.
Bifurcations - Troubleshooting
Enhance your knowledge of bifurcations and their troubleshooting techniques in this insightful lecture on complex systems analysis.
Phase Portraits from Potential Energy - Bifurcations - Constraint Forces from Lagrange Multipliers
Explore phase portraits, bifurcations, and constraint forces in dynamical systems. Learn graphical methods, analyze system behavior changes, and understand Lagrangian mechanics with practical applications.
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.
Bifurcations in 2D, Part 1 - Introduction, Saddle-Node, Pitchfork, Examples
Explore bifurcations in 2D systems, including saddle-node and pitchfork types. Learn how fixed points and closed orbits change with parameter variations, using examples from genetic regulatory systems.
Properties of Chaotic Systems for Audio
Explore chaotic systems for audio generation and transformation. Learn about fixed points, bifurcation, and practical applications with interactive visualizations and code examples.
Topics in Dynamical Systems - Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos
Explore dynamical systems: fixed points, linearization, manifolds, bifurcations, and chaos. Gain insights into nonlinear dynamics and their applications in describing our changing world.
Nonlinear Dynamics in an Age of Heuristic Science
Explore nonlinear dynamics through combinatorial topology, offering efficient computational methods and new perspectives for multiscale systems and data-driven science in biology and engineering.
Chimera States in Mechanical Oscillator Networks by Shashi Thutupalli
Explore chimera states in mechanical oscillator networks, covering synchronization, Kuramoto model, coupled populations, experimental designs, and various chimera phenomena in complex systems.
Dynamical Systems and Chaos - Interview with Stephen H. Kellert
Entrevista con Stephen H. Kellert sobre sistemas dinámicos y caos, explorando conceptos clave como bifurcaciones, el efecto mariposa y atractores extraños, y su relevancia en diversos campos científicos y humanísticos.
Dynamical Systems - Lecture 01
Explore fundamental concepts and applications of dynamical systems theory in this comprehensive lecture by mathematician Stefano Luzzatto.
Erik Lindgren: Infinity-Harmonic Potentials in Convex Rings
Exploration of Infinity-Laplace equation solutions in planar convex rings, focusing on streamline behavior, bifurcation phenomena, and regularity issues, with detailed analysis of a punctured square case.
Complex Dynamics in the Tropics - Partial Hyperbolicity in the Hénon Family
Explore partial hyperbolicity in Hénon family dynamics. Delve into complex mathematical concepts, including Henon-like maps, quadratic handle maps, and Julia sets.
Complexity Dynamics of Atopic Dermatitis System
Explore the complexity of atopic dermatitis through an in silico model, uncovering new oscillating behaviors and multistability patterns to enhance understanding and potential treatment strategies.
Noise-Driven Bifurcations in Neural Field Systems Modeling Grid Cell Networks
Explore noise-driven bifurcations in neural field systems, focusing on grid cell network modeling and their implications for spatial navigation.
Negative Drag and Symmetry-Breaking Motility in a Dilute Active Fluid
Explore negative drag and symmetry-breaking motility in dilute active fluids, examining continuous and discontinuous transitions in object velocity and critical phenomena in the mean-field Ising universality class.
Bifurcations and Multistability in Adaptive Vascular Networks
Explore bifurcations and multistability in adaptive vascular networks, uncovering complex dynamics and emergent behaviors in biological systems.