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/)