In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from one fixed point to three fixed points. Pitchfork bifurcations, like Hopf bifurcations have two types – supercritical and subcritical. In continuous dynamical systems described by ODEs—i.e. flows—pitchfork bifurcations occur generically in systems with symmetry. (Wikipedia).
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From playlist Geometry
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
Texture Sampling #2: Bilinear & Bicubic Samples
Following on from Part 1, I look at two common sampling methods that aim to reduce artefacts, bilinear and bicubic point sampling. The former linearly interpolates between neighbouring pixels, and the latter uses even further pixels to bias cubic splines to give a smoother contour between
From playlist Interesting Programming
CCSS What is an angle bisector
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
Constructing an Angle Bisector
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From playlist Geometry
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
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
Bead in a Rotating Hoop, Part 2: High Damping Limit
The dynamics of a bead in a rotating hoop when there is high damping reduce to a 1-dimensional differential equation, which can be analyzed graphically. The system undergoes a pitchfork bifurcation as a function of the rotation parameter. Some physical examples are shown, including the cen
From playlist Intermediate Classical Mechanics
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
Supercritical pitchfork bifurcation
Describes the supercritical pitchfork 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/different
From playlist Differential Equations with YouTube Examples
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
Explosive death in coupled oscillators by Manish Shrimali
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 W
From playlist Dynamics of Complex systems 2018
bisecting an angle with a compass - geometry constructions
In this video, I show how to bisect and angle with a compass and straightedge. This geometry construction uses ideas of congruent triangles, and the technique is useful for cutting an angle into two congruent angles. Outside of this computer software, this is my favorite type of compass t
From playlist Geometry
Perpendicular Bisector of a Line Segment and Triangle
This geometry video tutorial provides a basic introduction into the perpendicular bisector of a line segment and a triangle. it discusses the perpendicular bisector theorem and the definition of perpendicular bisectors in addition to how to use them in a geometry two column proof problem
From playlist Geometry Video Playlist
MAE5790-3 Overdamped bead on a rotating hoop
Equations of motion. When can we neglect the second derivative? Dimensional analysis and scaling. A singular limit. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Section 3.5.
From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University
ETH Lecture 08. Nonlinear Dynamics I: Bifurcations and Chaos (10/11/2011)
Course: Systems Dynamics and Complexity (Fall 2011) from ETH Zurich. Source: http://www.video.ethz.ch/lectures/d-mtec/2011/autumn/351-0541-00L.html
From playlist ETH Zürich: Systems Dynamics and Complexity (Fall 2011) | CosmoLearning Mathematics
MAE5790-2 One dimensional Systems
Linearization for 1-D systems. Existence and uniqueness of solutions. Bifurcations. Saddle-node bifurcation. Bifurcation diagrams. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 3.0--3.2, 3.4.
From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University
In this video, I define what it means to rearrange (or reshuffle) a series and show that if a series converges absolutely, then any rearrangement of the series converges to the same limit. Interesting Consequence: https://youtu.be/Mw7ocynGVmw Series Playlist: https://www.youtube.com/play
From playlist Series
Converting Complex Numbers From Trigonometric Form to Rectangular
Watch more videos on http://www.brightstorm.com/math/precalculus SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► ht
From playlist Precalculus
Harnessing the Universality of Tipping Points to Improve Early Warning Signal... by Chris Bauch
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)