Dynamical systems

Master stability function

In mathematics, the master stability function is a tool used to analyse the stability of the synchronous state in a dynamical system consisting of many identical oscillators which are coupled together, such as the Kuramoto model. The setting is as follows. Consider a system with identical oscillators. Without the coupling, they evolve according to the same differential equation, say where denotes the state of oscillator . A synchronous state of the system of oscillators is where all the oscillators are in the same state. The coupling is defined by a coupling strength , a matrix which describes how the oscillators are coupled together, and a function of the state of a single oscillator. Including the coupling leads to the following equation: It is assumed that the row sums vanish so that the manifold of synchronous states is neutrally stable. The master stability function is now defined as the function which maps the complex number to the greatest Lyapunov exponent of the equation The synchronous state of the system of coupled oscillators is stable if the master stability function is negative at where ranges over the eigenvalues of the coupling matrix . (Wikipedia).

Video thumbnail

Master Determing if a set of points is a Function or Not

Subscribe! http://www.freemathvideos.com Want more math video lessons? Visit my website to view all of my math videos organized by course, chapter and section. The purpose of posting my free video tutorials is to not only help students but allow teachers the resources to flip their classro

From playlist Functions #Master

Video thumbnail

Optimal control of spin systems with applications in (...) - D. Sugny - Workshop 2 - CEB T2 2018

Dominique Sugny (Univ. Bourgogne) / 05.06.2018 Optimal control of spin systems with applications in Magnetic Resonance Optimal control can be viewed as a generalization of the classical calculus of variations for problems with dynamical constraints. Optimal control was born in its modern

From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments

Video thumbnail

Fuzzy control of inverted pendulum

Fuzzy control of inverted pendulum, State-feedback controller is designed based on T-S fuzzy model with the consideration of system stability and performance.

From playlist Demonstrations

Video thumbnail

Everything You Need to Know About Control Theory

Control theory is a mathematical framework that gives us the tools to develop autonomous systems. Walk through all the different aspects of control theory that you need to know. Some of the concepts that are covered include: - The difference between open-loop and closed-loop control - How

From playlist Control Systems in Practice

Video thumbnail

Master Transformations of different parent functions

Subscribe! http://www.freemathvideos.com Want more math video lessons? Visit my website to view all of my math videos organized by course, chapter and section. The purpose of posting my free video tutorials is to not only help students but allow teachers the resources to flip their classro

From playlist Functions #Master

Video thumbnail

Closed loop stability lecture 2019-02-19

Discussion of the problems determining closed loop stability. The video I mention for the Nyquist criterion is here: https://youtu.be/3eYU8qIkp64

From playlist CPB Theme 2

Video thumbnail

Transfer Functions: Introduction and Implementation

In this video we introduce transfer functions and show how they can be derived from a set of linear, ordinary differential equations. We also examine how to use a transfer function to predict the output of system to a given input. Topics and time stamps: 0:38 – Example using an aircraft

From playlist Control Theory

Video thumbnail

Guanglian Li: Error analysis of a variational multiscale stabilization for convection-

Guanglian Li: Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Non-local Material Models and Concurrent Multiscale Metho

From playlist HIM Lectures: Trimester Program "Multiscale Problems"

Video thumbnail

M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem

The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in particular the idea to use surfaces of prescribed mean curvature (as opposed to minimal surfaces). Ha

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

Video thumbnail

M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem (vt)

The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in particular the idea to use surfaces of prescribed mean curvature (as opposed to minimal surfaces). Ha

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

Video thumbnail

Master How to determine the x and y intercepts of a rational function

I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. If I helped you in this video, I would love to have you subscribe. My subscribers are my

From playlist Rational Functions #Master

Video thumbnail

Lecture 16 | MIT 6.832 Underactuated Robotics, Spring 2009

Lecture 16: Introducing stochastic optimal control Instructor: Russell Tedrake See the complete course at: http://ocw.mit.edu/6-832s09 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.832 Underactuated Robotics, Spring 2009

Video thumbnail

Markov processes and applications-4 by Hugo Touchette

PROGRAM : BANGALORE SCHOOL ON STATISTICAL PHYSICS - XII (ONLINE) ORGANIZERS : Abhishek Dhar (ICTS-TIFR, Bengaluru) and Sanjib Sabhapandit (RRI, Bengaluru) DATE : 28 June 2021 to 09 July 2021 VENUE : Online Due to the ongoing COVID-19 pandemic, the school will be conducted through online

From playlist Bangalore School on Statistical Physics - XII (ONLINE) 2021

Video thumbnail

Florian Mehats: Stable and unstable steady states for the HMF model

CIRM VIRTUAL EVENT Recorded during the meeting "Kinetic Equations: from Modeling, Computation to Analysis" the March 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide m

From playlist Virtual Conference

Video thumbnail

DevOps Interview Questions | DevOps Interview Questions & Answers - 2023 | DevOps Tutorial | Edureka

🔥𝐄𝐝𝐮𝐫𝐞𝐤𝐚'𝐬 𝐃𝐞𝐯𝐎𝐩𝐬 𝐭𝐫𝐚𝐢𝐧𝐢𝐧𝐠 𝐩𝐫𝐨𝐠𝐫𝐚𝐦 (Use code "𝐘𝐎𝐔𝐓𝐔𝐁𝐄𝟐𝟎"): https://www.edureka.co/devops-certification-training This Edureka DevOps Interview Questions and Answers video ( DevOps Interview Blog : https://www.edureka.co/blog/interview-questions/top-devops-interview-questions/ ) will help y

From playlist DevOps Training Videos

Video thumbnail

Peter Zoller: Introduction to quantum optics - Lecture 4

Abstract: Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective

From playlist Mathematical Physics

Video thumbnail

A Blueprint of Standardized and Composable Machine Learning - Eric Xing

Seminar on Theoretical Machine Learning Topic: A Blueprint of Standardized and Composable Machine Learning Speaker: Eric Xing Affiliation: Carnegie Mellon University Date: August 6, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Random walk across the epigenetic landscape - Lecture 2 by Andràs Paldi

ORGANIZERS : Vidyanand Nanjundiah and Olivier Rivoire DATE & TIME : 16 April 2018 to 26 April 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This program is aimed at Master's- and PhD-level students who wish to be exposed to interesting problems in biology that lie at the biology-

From playlist Living Matter 2018

Video thumbnail

Master Graphing Rational Functions Part 5

Subscribe! http://www.freemathvideos.com Want more math video lessons? Visit my website to view all of my math videos organized by course, chapter and section. The purpose of posting my free video tutorials is to not only help students but allow teachers the resources to flip their classro

From playlist Rational Functions #Master

Related pages

Lyapunov exponent | Dynamical system | Ordinary differential equation | Kuramoto model | Stability theory