Oregonator

class otp.oregonator.OregonatorProblem

Bases: otp.Problem

A periodic, three-variable model for the Belousov–Zhabotinsky reaction.

The Oregonator chemical reaction [FN74] is given by

\[\begin{split} \ce{ A + Y &-> X + P \\ X + Y &-> 2P \\ A + X &-> 2X + 2Z \\ 2X &-> A + P \\ B + Z &-> 1/2 $f$ Y. } \end{split}\]

Species $\ce{A = BrO3-}$, $\ce{B = CH2(COOH)2}$, and $\ce{P = HOBr}$ or $\ce{BrCH(COOH)2}$ are assumed to be constant. The dynamic concentrations of intermediate species $\ce{X = HBrO2}$, $\ce{Y = Br-}$, and $\ce{Z = Ce(IV)}$ can be modeled by an ODE in three variables. Field and Noyes [FN74] proposed the nondimensionalized form

\[\begin{split} α' &= s(η - η α + α - q α^2), \\ η' &= s^{-1}(-η - η α + f ρ), \\ ρ' &= w (α - ρ), \end{split}\]

where $α$, $η$, and $ρ$ are scaled concentrations of $\ce{X}$, $\ce{Y}$, and $\ce{Z}$, respectively.

Notes

Type	ODE
Number of Variables	3
Stiff	typically, depending on $f$, $q$, $s$, and $w$

Example

>>> problem = otp.oregonator.presets.Canonical;
>>> sol = problem.solve();
>>> problem.plotPhaseSpace(sol, 'Vars', [2, 3]);

Constructor Summary

OregonatorProblem(timeSpan, y0, parameters)

Create a Oregonator problem object.

Parameters:

timeSpan (numeric(1, 2)) – The start and final time.
y0 (numeric(3, 1)) – The initial conditions.
parameters (OregonatorParameters) – The parameters.

Parameters

class otp.oregonator.OregonatorParameters

Bases: otp.Parameters

Parameters for the Oregonator problem.

Constructor Summary

OregonatorParameters(varargin)

Create an Oregonator parameters object.

Parameters:: varargin – A variable number of name-value pairs. A name can be any property of this class, and the subsequent value initializes that property.

Property Summary

F: The stoichiometric factor $f$.

Q: The reaction constant $q$.

S: The reaction constant $s$.

W: The reaction constant $w$.

Presets

class otp.oregonator.presets.Canonical

Bases: otp.oregonator.OregonatorProblem

The Oregonator configuration used in [HW96] (p. 144) called OREGO. It uses time span $t ∈ [0, 360]$, initial condition $y_0 = [1, 2, 3]^T$, and parameters

\[\begin{split} f &= 1, \\ q &= 8.375 \times 10^{-6}, \\ s &= 77.27, \\ w &= 0.1610. \end{split}\]

Constructor Summary

Canonical(varargin)

Create the canonical Oregonator problem object.

Parameters:

varargin –

A variable number of name-value pairs. The accepted names are

f – Value of $f$.
q – Value of $q$.
s – Value of $s$.
w – Value of $w$.

class otp.oregonator.presets.GottwaldWanner

Bases: otp.oregonator.OregonatorProblem

The Oregonator configuration from [GW82] which uses time span $t ∈ [0, 302.85805]$, initial condition $y_0 = [4, 1.331391, 2.852348]^T$, and parameters

\[\begin{split} f &= 1, \\ q &= 8.375 \times 10^{-6}, \\ s &= 77.27, \\ w &= 0.1610. \end{split}\]

The initial condition lies on a stable limit cycle, and the time span is chosen to be one period.

Constructor Summary

GottwaldWanner(): Create the Gottwald–Wanner Oregonator problem object.

class otp.oregonator.presets.EnrightHull

Bases: otp.oregonator.OregonatorProblem

The Oregonator configuration used in problem CHM 9 of [EH76]. It uses time span $t ∈ [0, 300]$, initial condition $y_0 = [4, 1.1, 4]^T$, and parameters

\[\begin{split} f &= 1, \\ q &= 8.375 \times 10^{-6}, \\ s &= 77.27, \\ w &= 0.1610. \end{split}\]

Constructor Summary

EnrightHull(): Create the Enright–Hull Oregonator problem object.