Autonomous

Nonlinear ODEs. Wrapper for emulator dynamical models

• Internal Emulators - in house ground truth equations

• External Emulators - third party models

References:

• https://en.wikipedia.org/wiki/List_of_nonlinear_ordinary_differential_equations

• https://en.wikipedia.org/wiki/List_of_dynamical_systems_and_differential_equations_topics

class autonomous.Autoignition(nsim=1001, ninit=0, ts=0.1, seed=59)

ODE describing pulsating instability in open-ended combustor.

• Koch, J., Kurosaka, M., Knowlen, C., Kutz, J.N., “Multiscale physics of rotating detonation waves: Autosolitons and modulational instabilities,” Physical Review E, 2021

equations(x, t)

Define equations defining the dynamical system

class autonomous.Brusselator1D(nsim=1001, ninit=0, ts=0.1, seed=59)

Brusselator

• https://en.wikipedia.org/wiki/Brusselator

equations(x, t)

Define equations defining the dynamical system

class autonomous.ChuaCircuit(nsim=1001, ninit=0, ts=0.1, seed=59)

Chua’s circuit

• https://en.wikipedia.org/wiki/Chua%27s_circuit

• https://www.chuacircuits.com/matlabsim.php

equations(x, t)

Define equations defining the dynamical system

class autonomous.DoublePendulum(nsim=1001, ninit=0, ts=0.1, seed=59)

Double Pendulum https://scipython.com/blog/the-double-pendulum/

equations(x, t)

Define equations defining the dynamical system

class autonomous.Duffing(nsim=1001, ninit=0, ts=0.1, seed=59)

Duffing equation

• https://en.wikipedia.org/wiki/Duffing_equation

equations(x, t)

Define equations defining the dynamical system

class autonomous.Lorenz96(nsim=1001, ninit=0, ts=0.1, seed=59)

Lorenz 96 model

• https://en.wikipedia.org/wiki/Lorenz_96_model

equations(x, t)

Define equations defining the dynamical system

class autonomous.LorenzSystem(nsim=1001, ninit=0, ts=0.1, seed=59)

Lorenz System

• https://en.wikipedia.org/wiki/Lorenz_system#Analysis

• https://ipywidgets.readthedocs.io/en/stable/examples/Lorenz%20Differential%20Equations.html

• https://scipython.com/blog/the-lorenz-attractor/

• https://matplotlib.org/3.1.0/gallery/mplot3d/lorenz_attractor.html

equations(x, t)

Define equations defining the dynamical system

class autonomous.LotkaVolterra(nsim=1001, ninit=0, ts=0.1, seed=59)

Lotka–Volterra equations, also known as the predator–prey equations

• https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations

equations(x, t)

Define equations defining the dynamical system

class autonomous.ODE_Autonomous(nsim=1001, ninit=0, ts=0.1, seed=59)

base class autonomous ODE

simulate(ninit=None, nsim=None, ts=None, x0=None)

Parameters:

• nsim – (int) Number of steps for open loop response

• ninit – (float) initial simulation time

• ts – (float) step size, sampling time

• x0 – (float) state initial conditions

Returns:

The response matrices, i.e. X

class autonomous.Pendulum(nsim=1001, ninit=0, ts=0.1, seed=59)

Simple pendulum.

• https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.odeint.html

equations(x, t)

Define equations defining the dynamical system

class autonomous.RosslerAttractor(nsim=1001, ninit=0, ts=0.1, seed=59)

Rössler attractor

• https://en.wikipedia.org/wiki/R%C3%B6ssler_attractor

equations(x, t)

Define equations defining the dynamical system

class autonomous.ThomasAttractor(nsim=1001, ninit=0, ts=0.1, seed=59)

Thomas’ cyclically symmetric attractor

• https://en.wikipedia.org/wiki/Thomas%27_cyclically_symmetric_attractor

equations(x, t)

Define equations defining the dynamical system

class autonomous.UniversalOscillator(nsim=1001, ninit=0, ts=0.1, seed=59)

Harmonic oscillator

• https://en.wikipedia.org/wiki/Harmonic_oscillator

• https://sam-dolan.staff.shef.ac.uk/mas212/notebooks/ODE_Example.html

equations(x, t)

Define equations defining the dynamical system

class autonomous.VanDerPol(nsim=1001, ninit=0, ts=0.1, seed=59)

Van der Pol oscillator

• https://en.wikipedia.org/wiki/Van_der_Pol_oscillator

• http://kitchingroup.cheme.cmu.edu/blog/2013/02/02/Solving-a-second-order-ode/

equations(x, t)

Define equations defining the dynamical system