rxnrate: Solving the right side of the gLV equations

In CoDaLoMic: Compositional Models to Longitudinal Microbiome Data

Solving the right side of the gLV equations

Description

This function calculates the right side of the gLV equation.

Usage

rxnrate(State, parms)

Arguments

State	Vector with a CoDa composition
parms	Matrix. Each row has the parameters of each differential equation. following our example, parms has the parameters placed as follows: r1 a11 a12 a13 r2 a21 a22 a23 r3 a31 a32 a33

Details

For instance, if we want to solve the following gLV equations:

\frac{dx_{1}(t)}{dt}=r_{1}\cdot x_{1}(t)+x_{1}(t)\cdot[a_{11}\cdot x_{1}(t)+a_{12}\cdot x_{2}(t)+a_{13}\cdot x_{3}(t)]

\frac{dx_{2}(t)}{dt}=r_{2}\cdot x_{2}(t)+x_{2}(t)\cdot[a_{21}\cdot x_{1}(t)+a_{22}\cdot x_{2}(t)+a_{23}\cdot x_{3}(t)]

\frac{dx_{3}(t)}{dt}=r_{3}\cdot x_{3}(t)+x_{3}(t)\cdot[a_{31}\cdot x_{1}(t)+a_{32}\cdot x_{2}(t)+a_{33}\cdot x_{3}(t)]

This function returns a vector with the value of:

r_{1}\cdot x_{1}(t)+x_{1}(t)\cdot[a_{11}\cdot x_{1}(t)+a_{12}\cdot x_{2}(t)+a_{13}\cdot x_{3}(t)]

r_{2}\cdot x_{2}(t)+x_{2}(t)\cdot[a_{21}\cdot x_{1}(t)+a_{22}\cdot x_{2}(t)+a_{23}\cdot x_{3}(t)]

r_{3}\cdot x_{3}(t)+x_{3}(t)\cdot[a_{31}\cdot x_{1}(t)+a_{32}\cdot x_{2}(t)+a_{33}\cdot x_{3}(t)]

Value

Returns a vector with the value of the right side of the gLV equations.

Examples

cinit1<-c(x1<-0.7,x2<-0.2,x3<-0.1)
parms1= cbind(c(0.1,0.2,-0.1),c(-0.2,0.1,-0.1),c(0.3,0.2,0.3),c(0.1,0.22,0.2))
rxnrate(cinit1,parms1)

CoDaLoMic documentation built on April 12, 2025, 2:18 a.m.