DOING PHYSICS WITH PYTHON

PYTHON

DYNAMICAL SYSTEMS

Ian Cooper

matlabvisualphysics@gmail.com

Please email me any comments, corrections, suggestions, additions

JASON BRAMBURGER YouTube lecture series on dynamical systems (Lx video ref)

DOWNLOAD DIRECTORIES FOR PYTHON CODE

Google drive

GitHub

ONE DIMENSIONAL DYNAMICAL SYSTEMS

Discrete dynamical systems with 1 degree of freedom

Logistic Difference Equation

Nonlinear [1D] dynamical system: fixed points, stability, bifurcations

Dynamical systems with 2 degrees of freedom: Predator-Prey systems (Lotka-Volterra equations)

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

[2D] linear dynamical systems

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

Nonlinear [2D] dynamical system: fixed points, stability, bifurcations

[2D] nonlinear dynamical systems

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

Lorenz equations: strange attractors (L27)

ANIMATION: Lorenz equations: strange attractors (L27)

A chaotic dynamical system: driven damped pendulum (a comprehensive analysis)

A minimal model for tumor growth and chemotherapy

MATHEMATICAL EPIDEMIOLOGY

The mSIR model for the spread of infectious diseases