COMBOS: Web App for Finding
Identifiable Parameter Combinations in...

ODEs: dx/dt = f(x,p,u), with Outputs: y = g(x,p)
Parameters p and f, x, p, y and u vectors

Guidelines for User Input

Naming conventions
TimeMUST BE "t"
State varsMUST BE "x" followed by a number, e.g. x1, x2, ...
InputsMUST BE "u" followed by a number, e.g. u1, u2, ...
OutputsMUST BE "y" followed by a number, e.g. y1, y2, ...
THE NUMBERING OF STATE VARS, INPUTS & OUTPUTS MUST ALWAYS START FROM 1 & BE MONOTONICALLY INCREASING, e.g. inputs appearing in any equation must begin with u1 (even if it's in the x2dot equation).
ParametersMUST BE any unreserved letter (NOT x,u,y,t) by itself or followed by any combination of letters, numbers, or commas, e.g. p  p4  Vmax  k12,34
Init CondsCAN BE defined for ANY existing state var and MUST BE expressed as a number or a function of the parameters, e.g. x2(0)=3*p1
Known constants MUST BE entered as numerical values; otherwise, they will be treated as unknown parameters.
Operands MUST BE separated by some combination of operators (+  -  *  /  ^) and regular parantheses, e.g. k0,1*x1+u1

Syntax rules
Enter mathematical equations using familiar ASCIIMathML notation

Results are provided in two forms:
1) All solutions (positive, negative, complex), not necessarily in simplest form. (Default)
2) Only positive solutions, in simplest form.

If You Have One, Copy/Paste Your File

Please enter equations in the following order: 1. ODEs, 2. Outputs, 3. Initial conditions, and separate equations by semicolons,
e.g. dx1/dt=k0,1*x1+u1; y1=x1/V; x1(0)=0



ODEs with Inputs Located

e.g. dx1/dt=k0,1*x1+u1

Output Equations

e.g. y1=x1/V


Try these examples!

  • 2-Comp Unidentifiable Model
  • 2-Comp Identifiable Model (k01 = 0)
  • 3-Comp Unidentifiable Model
  • 3-Comp Unidentifiable Model w/ ICs
  • 4-Comp Unidentifiable Model
  • 4-Comp Unidentifiable Model w/ ICs
  • 4-Comp Unidentifiable HIV Model *
  • © 2014 by UCLA Biocybernetics Laboratory, JJ DiStefano III, Director
    Algorithms by Nikki Meshkat (Math Biosci 2009, '11, '12)
    Web App by Christine Kuo
    Fine-Tuning by Sami Yerunkar
    Modified by Alejandro Rioja
    Version 1.5 November 2014 Please send comments, bugs, criticisms to:

    * Xia, X., & Moog, C. H. (2003). Identifiability of nonlinear systems with application to HIV/AIDS models.
    IEEE Trans. Autom. Control, 48(2), 330-336.