Python Scripts for 2D, 3D and 4D Flows
These Python programs can be downloaded from GitHub at https://github.itap.purdue.edu/nolte/Python-Programs-for-Nonlinear-Dynamics
DampedDriven.py Driven-damped oscillators. Options are: driven-damped pendulum and driven-damped double well potential. Plots a two-dimensional Poincaré section.
DoublePendulum.py Double pendulum.
Duffing.py Duffing oscillator.
DWH.py Biased double well.
Flow2D.py Simple flows for 2D autonomous dynamical systems. Options are: Medio, van der Pol, and Fitzhugh-Nagumo models.
Flow2DBorder.py Same as Flow2D.py but with initial conditions set on the boarder of the phase portrait.
Flow3D.py Flows for 3D autonomous dynamical systems. Options are: Lorenz, Rössler and Chua’s Circuit.
gravlens.py Gravitational lensing
Hamilton4D.py Hamiltonian flows for 4D autonomous systems. Options are: Henon-Heiles potential, and the crescent potential. Plots a two-dimensional Poincaré section.
Heiles.py Henon-Heiles and also a crescent model
HenonHeiles.py Standalone Henon-Heiles model.
Hill.py Hill potentials for 3-body problem.
Kuramoto.py Kuramoto synchronization of phase oscillators on a complete graph.
logistic.py Logistic discrete map, plus some other choices.
Lozi.py Discrete iterated Lozi map conserves volume.
NetDynamics.py Coupled phase oscillators on various network topologies. Has more options than coupleNdriver.py.
NetSIR.py SIR viral infection model on networks
NetSIRS.py SIRS viral infection model on networks
PenInverted.py Inverted pendulum.
Perturbed.py Driven undampded oscillators with a plane-wave perturbation. Options are: pendulum and double-well potential. These are driven nonlinear Hamiltonian systems. When driven at small perturbation amplitude near the separatrix, chaos emerges. These systems do not conserve energy, because there is a constant input and output of energy as the system reacts against the drive force. Plots a two-dimensional Poincaré section.
raysimple.py Eikonal equation simulator.
SIR.py SIR homogeneous COVID-19 model
SIRS.py SIRS homogeneous COVID-19 model
SIRWave.py Covid-19 second wave model
StandMap.py The Chirikov map, also known as the standard map, is a discrete itereated map with winding numbers and islands of stability.
StandMapHom.py Homoclinic tangle for the standard map.
StandMapTwist.py The Standard Map in twist format
trirep.py Replicator dynamics in 3D simplex format.
UserFunction.py Growing library of user functions linfit.py – linear regression function
WebMap.py The discrete map of a periodically kicked oscillator displays a web of dynamics.
(Selected Python programs can be found at the Galileo Unbound Blog Site: https://galileo-unbound.blog/tag/python-code/)