Bifurcation theory | Nonlinear systems
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them with motif. (Wikipedia).
Mathematical model of a fishery
In a model of a fishery, bifurcation theory is used to understand how the fish population depends on the rate at which fish are caught. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https:
From playlist Differential Equations
What is a Bipartite Graph? | Graph Theory
What is a bipartite graph? We go over it in today’s lesson! I find all of these different types of graphs very interesting, so I hope you will enjoy this lesson. A bipartite graph is any graph whose vertex set can be partitioned into two disjoint sets (called partite sets), such that all e
From playlist Graph Theory
Describes the transcritical bifurcation using the differential equation of the normal form. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differential-equati
From playlist Differential Equations with YouTube Examples
Trigonometry 5 The Cosine Relationship
A geometrical explanation of the law of cosines.
From playlist Trigonometry
Subcritical pitchfork bifurcation
Describes the subcritical pitchfork bifurcation using the differential equation of the normal form. Free books: http://bookboon.com/en/differential-equations-with-youtube-examples-ebook http://www.math.ust.hk/~machas/differential-equations.pdf
From playlist Differential Equations with YouTube Examples
Graph Theory: 09. Graph Isomorphisms
In this video I provide the definition of what it means for two graphs to be isomorphic. I illustrate this with two isomorphic graphs by giving an isomorphism between them, and conclude by discussing what it means for a mapping to be a bijection. An introduction to Graph Theory by Dr. Sar
From playlist Graph Theory part-2
Rahul Savani: Polymatrix Games Algorithms and Applications
Polymatrix games are multi-player games that capture pairwise interactions between players. They are defined by an underlying interaction graph, where nodes represent players, and every edge corresponds to a two-player strategic form (bimatrix) game. This talk will be a short survey that w
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
Injective, Surjective and Bijective Functions (continued)
This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.
From playlist Foundational Math
What are Complete Bipartite Graphs? | Graph Theory, Bipartite Graphs
What are complete bipartite graphs? We'll define complete bipartite graphs and show some examples and non-examples in today's video graph theory lesson! Remember a graph G = (V, E) is bipartite if the vertex set V can be partitioned into two sets V1 and V2 (called partite sets) such that
From playlist Graph Theory
Dynamics of piecewise smooth maps (Lecture 4) by Paul Glendinnng
PROGRAM : DYNAMICS OF COMPLEX SYSTEMS 2018 ORGANIZERS : Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE: 16 June 2018 to 30 June 2018 VENUE: Ramanujan hall for Summer School held from 16 - 25 June, 2018; Madhava hall for
From playlist Dynamics of Complex systems 2018
Rate-Induced Tipping in Asymptotically Autonomous Dynamical Systems: Theory.. by Sebastian Wieczorek
PROGRAM TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID) ORGANIZERS: Partha Sharathi Dutta (IIT Ropar, India), Vishwesha Guttal (IISc, India), Mohit Kumar Jolly (IISc, India) and Sudipta Kumar Sinha (IIT Ropar, India) DATE: 19 September 2022 to 30 September 2022 VENUE: Ramanujan Lecture Hall an
From playlist TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID, 2022)
Jaroen Lamb - Towards a bifurcation theory of random dynamical systems - IPAM at UCLA
Recorded 01 September 2022. Jeroen Lamb of Imperial College London Mathematics presents "Towards a bifurcation theory of random dynamical systems" at IPAM's Reconstructing Network Dynamics from Data: Applications to Neuroscience and Beyond. Abstract: Most of dynamical systems theory concer
From playlist 2022 Reconstructing Network Dynamics from Data: Applications to Neuroscience and Beyond
Christian Kuehn (7/25/22): Dynamical Systems for Deep Neural Networks
Abstract: In this talk, I am going to explain several approaches to explain the geometry and dynamics of neural networks. First, I will show, why neural networks should always be viewed within the framework of dynamical systems. Then I am going to show how to employ rigorous validated comp
From playlist Applied Geometry for Data Sciences 2022
Theodore Vo: Canards, Cardiac Cycles, and Chimeras
Abstract: Canards are solutions of singularly perturbed ODEs that organise the dynamics in phase and parameter space. In this talk, we explore two aspects of canard theory: their applications in the life sciences and their ability to generate new phenomena. More specifically, we will use
From playlist SMRI Seminars
Simple Examples of Rate and Bifurcation Tipping by Sebastian Wieczorek
PROGRAM TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID) ORGANIZERS: Partha Sharathi Dutta (IIT Ropar, India), Vishwesha Guttal (IISc, India), Mohit Kumar Jolly (IISc, India) and Sudipta Kumar Sinha (IIT Ropar, India) DATE: 19 September 2022 to 30 September 2022 VENUE: Ramanujan Lecture Hall an
From playlist TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID, 2022)
MAE5790-12 Bifurcations in two dimensional systems
Bifurcations of fixed points: saddle-node, transcritical, pitchfork. Hopf bifurcations. Other bifurcations of periodic orbits. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 8.0--8.2.
From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University
Foundational Concepts In Chaos Theory: An Explanation of Veritasium's Logistic Map Video
In This video I'll go over the foundations of chaos theory to and you'll learn how to prove and predict certain aspects of the Logistic Map. This video was also done with inspiration from 3blue1brown's summer 2021 some1 exposition! Link to Veritasium's Video: https://www.youtube.com/wat
From playlist Summer of Math Exposition Youtube Videos
Bifurcation and Catastrophy theory: Physical and Natural systems by Petri Piiroinen
Modern Finance and Macroeconomics: A Multidisciplinary Approach URL: http://www.icts.res.in/program/memf2015 DESCRIPTION: The financial meltdown of 2008 in the US stock markets and the subsequent protracted recession in the Western economies have accentuated the need to understand the dy
From playlist Modern Finance and Macroeconomics: A Multidisciplinary Approach
Dynamical systems, fractals and diophantine approximations – Carlos Gustavo Moreira – ICM2018
Plenary Lecture 6 Dynamical systems, fractal geometry and diophantine approximations Carlos Gustavo Moreira Abstract: We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related
From playlist Plenary Lectures
From playlist Graph Theory