# 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**

__Time__ | MUST BE "t" |

__State vars__ | MUST BE "x" followed by a number, e.g. x1, x2, ... |

__Inputs__ | MUST BE "u" followed by a number, e.g. u1, u2, ... |

__Outputs__ | MUST 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).** |

__Parameters__ | MUST 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 Conds__ | CAN 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

**Note**

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

## Try these examples!

2-Comp Unidentifiable Model
2-Comp Identifiable Model (k_{01} = 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: joed@ucla.edu

* Xia, X., & Moog, C. H. (2003). Identifiability of nonlinear systems with application to HIV/AIDS models.

IEEE Trans. Autom. Control, 48(2), 330-336.