Hidden oscillation | Chaos theory | Nonlinear systems | Dynamical systems
In the bifurcation theory, a bounded oscillation that is born without loss of stability of stationary set is called a hidden oscillation. In nonlinear control theory, the birth of a hidden oscillation in a time-invariant control system with bounded states means crossing a boundary, in the domain of the parameters, where local stability of the stationary states implies global stability (see, e.g. Kalman's conjecture). If a hidden oscillation (or a set of such hidden oscillations filling a compact subset of the phase space of the dynamical system) attracts all nearby oscillations, then it is called a hidden attractor. For a dynamical system with a unique equilibrium point that is globally attractive, the birth of a hidden attractor corresponds to a qualitative change in behaviour from monostability to bi-stability. In the general case, a dynamical system may turn out to be multistable and have coexisting local attractors in the phase space. While trivial attractors, i.e. stable equilibrium points, can be easily found analytically or numerically, the search of periodic and chaotic attractors can turn out to be a challenging problem (see, e.g. the second part of Hilbert's 16th problem). (Wikipedia).
There's a strange place in the sky where everything is attracted. And unfortunately, it's on the other side of the Milky Way, so we can't see it. What could be doing all this attracting?
From playlist Guide to Space
Dark Matter: The Unknown Force
Dark Matter: The Unknown Force - Dark Matter Explained Go to https://squarespace.com/aperture to get a free trial and 10% off your first purchase. Join the community Discord!: https://discord.gg/Aperture Dark Matter is an enigma that thousands of physicists are trying to figure out each a
From playlist Science & Technology 🚀
If you're not sure what a black hole is, or even if you just need a quick refresher, Brian Greene explains what lies behind these cosmological powerhouses. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us o
From playlist Science Unplugged: Black Holes
The Attractiveness Of Magnetic Fields
What causes a material to be magnetic? License: Creative Commons BY-NC-SA More information at http://k12videos.mit.edu/terms-conditions
From playlist Physics
Magnetism (1 of 13) Magnets & Magnetic Field Lines, An Explanation
An explanation of magnets and how to draw magnetic field lines. Covers force of attraction and repulsion. How to draw magnetic field lines for like poles (bar magnet), unlike poles and a U-shaped magnet. A magnet is a material or object that produces a magnetic field. This magnetic fiel
From playlist Magnets, Magnetism and Charges in Magnetic Fields
Science Bulletins: Elusive Y-Dwarfs Discovered
Brown dwarfs are cosmic objects that are intermediate between stars and planets. Scientists have spent more than a decade seeking confirmation of the coolest, faintest type of brown dwarfs—Y-dwarfs—which had been predicted but never seen. Recently, the powerful infrared vision of NASA's Wi
From playlist Science Bulletins
Dipole Dipole Forces of Attraction - Intermolecular Forces
This chemistry video tutorial provides a basic introduction into dipole dipole forces of attraction. A dipole is a molecule that contains a permanent separation of charge. One side of the molecule may have a partial positive charge while the other side may contain a partial negative char
From playlist New AP & General Chemistry Video Playlist
Lecture 7/16 : Recurrent neural networks
Neural Networks for Machine Learning by Geoffrey Hinton [Coursera 2013] 7A Modeling sequences: A brief overview 7B Training RNNs with backpropagation 7C A toy example of training an RNN 7D Why it is difficult to train an RNN 7E Long term short term memory
From playlist Neural Networks for Machine Learning by Professor Geoffrey Hinton [Complete]
Lecture 7D : Why it is difficult to train an RNN
Neural Networks for Machine Learning by Geoffrey Hinton [Coursera 2013] Lecture 7D : Why it is difficult to train an RNN
From playlist Neural Networks for Machine Learning by Professor Geoffrey Hinton [Complete]
Lecture 7.4 — Why it is difficult to train an RNN? [Neural Networks for Machine Learning]
Lecture from the course Neural Networks for Machine Learning, as taught by Geoffrey Hinton (University of Toronto) on Coursera in 2012. Link to the course (login required): https://class.coursera.org/neuralnets-2012-001
From playlist [Coursera] Neural Networks for Machine Learning — Geoffrey Hinton
Magnetism (2 of 13) Why are Magnets Magnetic, An Explanation
An explanation of why magnets are magnetic. Ever wondered why some pieces of metal stick together and some don't? Watch this video and find out why. It is amazing. A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for t
From playlist Magnets, Magnetism and Charges in Magnetic Fields
Huge Hidden Galactic Structure Found In The Zone of Avoidance Behind Milky Way
Get a Wonderful Person Tee: https://teespring.com/stores/whatdamath More cool designs are on Amazon: https://amzn.to/3wDGy2i Alternatively, PayPal donations can be sent here: http://paypal.me/whatdamath Hello and welcome! My name is Anton and in this video, we will talk about a discovery
From playlist Galaxies, Quasars, Blazars
Show Me Some Science! The Greenhouse Effect
What makes a gas a "Greenhouse Gas"? Little Shop of Physics investigates different gasses with a thermal camera to see if they radiate thermal radiation. Water, carbon dioxide and diflouroethane are greenhouse gasses. Air (mostly nitrogen and oxygen) are not.
From playlist Show Me Some Science!
Deep Learning of Dynamics and Coordinates with SINDy Autoencoders
This video by Kathleen Champion describes a new approach for simultaneously discovering models and an effective coordinate system using a custom SINDy autoencoder. Paper at PNAS: https://www.pnas.org/content/116/45/22445.abstract Kathleen Champion, Bethany Lusch, J. Nathan Kutz, Steven L
From playlist Research Abstracts from Brunton Lab
Luca Mazzucato - Computational Principles Underlying the Temporal Organization of Behavior
Naturalistic animal behavior exhibits a striking amount of variability in the temporal domain along at least three independent axes: hierarchical, contextual, and stochastic. First, a vast hierarchy of timescales links movements into behavioral sequences and long-term activities, from mill
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Marc Hoyois: Hilbert schemes in motivic homotopy theory
29 September 2021 Abstract: Hilbert schemes of ane spaces are highly singular schemes with a complicated geometry, but they exhibit some interesting stability phenomena as the dimension of the affine space goes to infinity. I will explain a computation of the motives of these Hilbert sche
From playlist Representation theory's hidden motives (SMRI & Uni of MĂĽnster)
Robert Cass: Perverse mod p sheaves on the affine Grassmannian
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From playlist Representation theory's hidden motives (SMRI & Uni of MĂĽnster)
Magnets are highly misunderstood, and often interpreted as magic. But they're not magic! It's just science. Let's learn about what magnets are and what produces magnetism and magnetic fields so that we can sound super smart at dinner parties, yes? Watch the whole Classical Physics playlis
From playlist Classical Physics