Estimating the Parameter 'a' from ODE System

Click For Summary
SUMMARY

The discussion focuses on estimating the parameter 'a' from a system of ordinary differential equations (ODEs) defined as x1_dot=f1(t)-ax1, x2_dot=f2(t)-ax2, and x3_dot=f3(t)-ax3. The nonlinear functions f1, f2, and f3 are unknown, while the initial conditions are provided as x1(0)=x2(0)=x3(0)=1. Participants emphasize the necessity of having initial values at a specific time to effectively estimate the parameter 'a'. The conversation highlights the importance of understanding the system's dynamics and the role of initial conditions in parameter estimation.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with nonlinear function analysis
  • Knowledge of parameter estimation techniques
  • Basic skills in numerical methods for solving ODEs
NEXT STEPS
  • Research methods for estimating parameters in ODE systems
  • Learn about initial value problems in differential equations
  • Explore numerical techniques for solving nonlinear ODEs
  • Study the use of software tools like MATLAB or Python's SciPy for ODE analysis
USEFUL FOR

Mathematicians, engineers, and researchers involved in modeling dynamic systems, particularly those working with ordinary differential equations and parameter estimation techniques.

Bita_La
Messages
2
Reaction score
0
Hi everyone
I have a system of ODE as follows
x1_dot=f1(t)-ax1
x2_dot=f2(t)-ax2
x3_dot=f3(t)-ax3

f1,2,3(t) are unknown nonlinear functions of time, a is constant and unknown, x1,2,3 and their derivatives are given. How can I estimate the parameter a from the given information?
Thanks
 
Physics news on Phys.org
Bita_La said:
Hi everyone
I have a system of ODE as follows
x1_dot=f1(t)-ax1
x2_dot=f2(t)-ax2
x3_dot=f3(t)-ax3

f1,2,3(t) are unknown nonlinear functions of time, a is constant and unknown, x1,2,3 and their derivatives are given. How can I estimate the parameter a from the given information?
Thanks
It's not clear what information you are given, besides the form of the equations. Do you have some initial values given which occur at a certain time t ?
 
SteamKing said:
It's not clear what information you are given, besides the form of the equations. Do you have some initial values given which occur at a certain time t ?
SteamKing said:
It's not clear what information you are given, besides the form of the equations. Do you have some initial values given which occur at a certain time t ?
Thanks for your reply. Yes, I know x1(0)=x2(0)=x3(0)=1
 

Similar threads

Graduate How can the stability of an ODE system be determined without solving it?
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad 2nd order ODE's, variation of parameters and the notorious constraint
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Stability for a system of nonlinear ODEs
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Qualitative implications of parameter shift in non-autonomous ODE
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Show positivity and boundedness of a non-linear system
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Can Nonlinear Equations be Linearized Using Free Parameters?
  • · Replies 4 ·
Replies
4
Views
2K
Maple How to get my function from these dsolve results
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Consequences on a system of ODEs after performing operations
  • · Replies 4 ·
Replies
4
Views
1K
Estimating damped harmonic oscillator parameters from this plot of the oscillations
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Analyzing a System of Nonlinear ODEs in Biology
  • · Replies 2 ·
Replies
2
Views
6K