|
DOING PHYSICS WITH PYTHON
PYTHON
DYNAMICAL
SYSTEMS
Complete
lecture course
Ian Cooper
matlabvisualphysics@gmail.com
Please email me any comments, corrections,
suggestions, additions
This website is under construction – additional topics are
continually being added
The lecture
course closely follows
JASON BRAMBURGER
YouTube lecture series on dynamical systems (Lx video ref)
DOWNLOAD DIRECTORIES FOR PYTHON CODE
Google
drive
GitHub
ONE DIMENSIONAL DYNAMICAL SYSTEMS
Introduction to Dynamical systems (L1)
The geometry of flows on the line (L2)
Fixed points and stability (L3)
Existence and Uniqueness (L4)
Potential (L5)
Saddle Node Bifurcations (L6)
Transcritical Bifurcations
(L7)
Pitchfork Bifurcations (L8)
Imperfect Pitchfork Bifurcations (L9)
Population dynamics 1: Bifurcations in a Model for Insect
Outbreak (L10)
Population dynamics 2: Exponential growth and the
logistics equation (L10)
Population
dynamics 3: A minimal model for tumor growth and chemotherapy (L10)
Flow on a circle (L11)
Ghosts
and bottlenecks (L12)
Modelling firefly
entrainment (L13)
TWO DIMENSIONAL LINEAR DYNAMICAL
SYSTEMS
Planar
[2D] linear dynamical systems: Theoretical considerations
Examples:
Multiple fixed points: Real eigenvalues, one eigenvalue equal to
zero
Examples:
Single fixed point at Origin: Real
non-zero eigenvalues
Examples:
Single fixed point at Origin: Complex eigenvalues
Mass – Spring system (L14)
TWO DIMENSIONAL NON-LINEAR DYNAMICAL
SYSTEMS
[2D]
non-linear dynamical systems: Theoretical considerations
System
with real eigenvalues
System
with complex eigenvalues
Rabbits
and Sheep population dynamics (L17)
Conservative
systems: Double potential well (L18)
Damped
Simple Pendulum (L19)
Van
der Pol Oscillator and limit cycles (L21)
Gradient
dynamical systems (L22, L23)
Saddle-node
bifurcations
Saddle-node
bifurcations in planar systems (L25)
Transcritical bifurcations
Pitchfork
bifurcations
Pitchfork bifurcations in planar systems (L25)
Supercritical
Hopf bifurcations
Subcritical
Hopf bifurcations
Homoclinic-node
bifurcations
|