README.md

Python-Programs

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

• DWH.py:

  • Biased double well.

• 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. (See: https://galileo-unbound.blog/2020/10/18/the-ups-and-downs-of-the-compound-double-pendulum/)

• Duffing.py:

  • Duffing oscillator.

• FlipPhone.py:

  • Flipping iPhone simulator. (See https://galileo-unbound.blog/2021/10/10/physics-of-the-flipping-iphone-and-the-fate-of-the-earth/.)

• 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.

• GravSynch.py:

  • Synchronization of clocks in a spaceship near a black hole. (See: https://galileo-unbound.blog/2021/05/16/locking-clocks-in-strong-gravity/)

• gravlens.py:

  • Gravitational lensing. (See: https://galileo-unbound.blog/2021/04/05/the-lens-of-gravity-einsteins-rings/)

• Hamilton4D.py:

  • Hamiltonian flows for 4D autonomous systems. Options are: Henon-Heiles potential, and the crescent potential. Plots a two-dimensional Poincaré section. (See: https://galileo-unbound.blog/2019/11/04/the-physics-of-life-the-universe-and-everything-in-one-easy-equation/)

• Heiles.py:

  • Henon-Heiles and also a crescent model

• HenonHeiles.py:

  • Standalone Henon-Heiles model.

• Hill.py:

  • Hill potentials for 3-body problem. (See: https://galileo-unbound.blog/2019/07/19/getting-armstrong-aldrin-and-collins-home-from-the-moon-apollo-11-and-the-three-body-problem/)

• Kuramoto.py:

  • Kuramoto synchronization of phase oscillators on a complete graph. (See: https://galileo-unbound.blog/2019/11/04/the-physics-of-life-the-universe-and-everything-in-one-easy-equation/)

• 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. (See: https://galileo-unbound.blog/2020/09/14/up-side-down-physics-dynamic-equilibrium-and-the-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. (See: https://galileo-unbound.blog/2019/05/30/the-iconic-eikonal-and-the-optical-path/)

• SIR.py:

  • SIR homogeneous COVID-19 model (See: https://galileo-unbound.blog/2020/03/22/physics-in-the-age-of-contagion-the-bifurcation-of-covid-19/)

• SIRS.py:

  • SIRS homogeneous COVID-19 model (See: https://galileo-unbound.blog/2020/07/20/physics-in-the-age-of-contagion-part-4-fifty-shades-of-immunity-to-covid-19/)

• SIRWave.py:

  • Covid-19 second wave model (See:https://galileo-unbound.blog/2020/04/06/physics-in-the-age-of-contagion-part-2-the-second-wave-of-covid-19/)

• 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. (See: https://galileo-unbound.blog/2020/08/24/henri-poincare-and-his-homoclinic-tangle/)

• StandMapTwist.py:

  • The Standard Map in twist format (See: https://galileo-unbound.blog/2019/10/14/how-number-theory-protects-you-from-the-chaos-of-the-cosmos/)

• trirep.py:

  • Replicator dynamics in 3D simplex format. (See: https://galileo-unbound.blog/2019/11/04/the-physics-of-life-the-universe-and-everything-in-one-easy-equation/)

• 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. (See: https://galileo-unbound.blog/2018/10/27/how-to-weave-a-tapestry-from-hamiltonian-chaos/)

(Selected Python programs can be found at the Galileo Unbound Blog Site: https://galileo-unbound.blog/tag/python-code/)