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

 

Saddle-node bifurcations

 

Transcritical bifurcations

 

Pitchfork bifurcations

 

Supercritical Hopf bifurcations

 

Subcritical Hopf bifurcations

 

Homoclinic-node bifurcations

 

 

 

 

 

 

 

 

 

 

 

 

 

Counters