Estimating the Parameter 'a' from ODE System

In summary, the conversation is about a system of ODE with unknown nonlinear functions and a constant, unknown parameter a. The values of x1, x2, and x3, as well as their derivatives, are given, but the parameter a needs to be estimated. The person asking the question also mentions having initial values for x1, x2, and x3.
  • #1
Bita_La
2
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
  • #2
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 ?
 
  • #3
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
 

1. How do you estimate the parameter 'a' from an ODE system?

To estimate the parameter 'a' from an ODE system, you can use various methods such as the least squares method, maximum likelihood estimation, or Bayesian estimation. These methods involve minimizing the error between the observed data and the model predictions to find the most likely value of 'a'.

2. What is the importance of estimating the parameter 'a' in an ODE system?

The parameter 'a' in an ODE system represents a key characteristic of the system and can greatly influence the behavior of the system. Estimating this parameter accurately is crucial for understanding and predicting the dynamics of the system.

3. Can you estimate the parameter 'a' from limited or noisy data?

Yes, it is possible to estimate the parameter 'a' from limited or noisy data. However, the accuracy of the estimation may be affected by the quality and quantity of the data. Advanced estimation techniques can also be used to improve the accuracy of the estimation.

4. Is it necessary to have prior knowledge about the system to estimate the parameter 'a'?

Having prior knowledge about the system can be helpful in estimating the parameter 'a', but it is not always necessary. Some estimation methods, such as maximum likelihood estimation, do not require prior knowledge and can still produce reliable estimates.

5. Can the estimated value of 'a' change over time in an ODE system?

Yes, the estimated value of 'a' can change over time in an ODE system. This can happen due to various reasons, such as changes in the system's environment, experimental conditions, or model assumptions. Therefore, it is important to regularly update and validate the estimated parameter values.

Similar threads

A How can the stability of an ODE system be determined without solving it?
    • Differential Equations
Replies
7
Views
2K
MHB Dimensional reduction of system of ODEs
    • Differential Equations
Replies
1
Views
1K
A Stability for a system of nonlinear ODEs
    • Differential Equations
Replies
9
Views
2K
ODE -> Transfer Function Assistance
    • Differential Equations
Replies
2
Views
1K
I Real ODE yields real solution through complex numbers
    • Differential Equations
Replies
3
Views
2K
I A common 2nd order ODE from dynamics but....
    • Differential Equations
Replies
8
Views
1K
System of two second order ODE's
    • Differential Equations
Replies
6
Views
1K
How to construct nonlinear ODE systems with given condition?
    • Differential Equations
Replies
1
Views
2K
Qualitative implications of parameter shift in non-autonomous ODE
    • Differential Equations
Replies
1
Views
2K
Maple How to get my function from these dsolve results
    • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top