Differential Eqs Lecture #8, Bifurcations, Linear Equations, Undetermined Coefficients, and Flows

preview_player
Показать описание

Lecture 8.

(0:00) Exam 1 information.
(3:05) Phase line and bifurcation examples, both by hand, and visualized on Mathematica.
(28:38) Linear Differential Equations and the Method of Undetermined Coefficients (a.k.a. "Educated Guessing").
(40:14) The "Full Solution" and the flow function for a simple autonomous differential equation

AMAZON ASSOCIATE
As an Amazon Associate I earn from qualifying purchases.
  1. Bill Kinney
  2. Method Of Undetermined Coefficients
  3. Bifurcation Diagram
  4. Bifurcation Theory
  5. bifurcation value
  6. phase line
Рекомендации по теме
Differential Eqs Lecture 0:50:46

Differential Eqs Lecture #8, Bifurcations, Linear Equations, Undetermined Coefficients, and Flows

Bifurcations of a 0:09:57

Bifurcations of a differential equation

Diff Eqs Lecture 0:49:30

Diff Eqs Lecture #9, Bifurcations, Undetermined Coefficients, Integrating Factors, Flows & Flow ...

ODE | Bifurcation 0:05:33

ODE | Bifurcation diagrams

Diff Eqs #7, 0:51:02

Diff Eqs #7, Implicit Solutions, Logistic Model w/ Harvesting, Bifurcations, Existence & Uniquen...

Ordinary Differential Equations. 0:06:01

Ordinary Differential Equations. Chapter 8, Lecture 3. Pitchfork bifurcation.

Ordinary Differential Equations. 0:06:48

Ordinary Differential Equations. Chapter 8, Lecture 1. Saddle-node bifurcation.

Ordinary Differential Equations. 0:04:59

Ordinary Differential Equations. Chapter 8, Lecture 4. The nature of bifurcation of equilibria.

Ordinary Differential Equations. 0:05:14

Ordinary Differential Equations. Chapter 8, Lecture 2. Transcritical bifurcation.

MA30060 Lecture 8 0:45:09

MA30060 Lecture 8 (20-21): transcritical and pitchfork bifurcations

Bifurcations (graphical method) 0:11:10

Bifurcations (graphical method) (full video)

Diff Eq video 0:08:39

Diff Eq video Bifurcation Points and Phase Lines

Bifurcations and bifurcation 0:44:01

Bifurcations and bifurcation diagrams

Phase Lines and 0:30:03

Phase Lines and Bifurcations

ODE | Phase 0:05:54

ODE | Phase diagrams

Diff Eqs & 1:07:00

Diff Eqs & Lin Alg: Nonlinear System Bifurcation, Hamiltonian & Gradient Systems, Diagonaliz...

Miniquiz bifurcation diagram 0:03:07

Miniquiz bifurcation diagram

Supercritical pitchfork bifurcation 0:10:44

Supercritical pitchfork bifurcation

Differential Equations - 0:11:58

Differential Equations - Topic Video - Bifurcation Diagrams

412 24 Center 0:17:38

412 24 Center Manifold for a Hopf Bifurcation

Diff Eqs Lecture 0:46:16

Diff Eqs Lecture #29, Phase Plane for a Complicated Competing Species Model

BIFURCATION: Pitchfork 0:00:33

BIFURCATION: Pitchfork

Normal Forms and 0:19:23

Normal Forms and Imperfections

412 35 Bifurcations 0:36:03

412 35 Bifurcations in Partial Differential Equations

Комментарии
Автор

Awesome lecture, do you have anymore examples on setting up bifurcation diagrams, they are really helpful?

AllenAK
Автор

Great lecture! Very well explained. I wish my school let us record lectures so we can go over the material that we may have not understood. Would you be willing to post your Wolfram notebooks to help better understand these differential equations? 

AcTommyX
Автор

Oh yeah, on your quadratic bifurcation equation, is that point at y=0 suppose to be there? I do not believe y=0 is one of the equilibrium solutions. 

AcTommyX