Steady State Examples - Revision history

Axec@dote.ru at 11:09, 19 August 2021

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Axec@dote.ru at 11:01, 19 August 2021

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Axec@dote.ru: Created page with "Steady state analysis of the mathematical model comprising system of ordinary differential equations
dY/dt = f(X, t), Y(0) = Y0
implies finding X_SS..."

2021-08-19T11:01:03Z

Created page with "Steady state analysis of the mathematical model comprising system of ordinary differential equations <center>dY/dt = f(X, t), Y(0) = Y0 </center> implies finding X_SS..."

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Steady state analysis of the mathematical model comprising system of ordinary differential equations 
<center>dY/dt = f(X, t), Y(0) = Y0 </center>
 implies finding X_SS and t such that f(X_SS, t) = 0, t > t_SS. 

In BioUML we have two analyses in that regard.

1. Algebraic steady state.

We transform the model to algebraic form F(X, t)=0 and solve this algebraic system.
Available solvers:
<ul>
<li>Levenberg Marquard algorithm
<li>Newton method
<li>Conjugate gradient
<li>KinSolver
</ul>

Of course this algebaric system may have no solution or more than one solution - in the latter case BioUML will find only one of them.

In order to run Algebraic steady state analysis go to Analysis tab in the repository tree, select Methods then Differential algebraic equations 
The very first analysis in the list would be Algebraic steady state analysis .
User should set diagram for which steady state should be found and form of the result (table with parameter values or Simulation result).
Example of analysis with parameters set is presented on the Fig. 1.
[[algebraic_steady_state_analysis_example.png|thumb|Fig.1 Example of Algebraic Steady State Analysis]]

2. Steady state.
In this case we simply simulate the model from given initial values Y0 until Y stops changing in time.

In order to run Steady state analysis go to Analysis tab in the repository tree, select Methods then Differential algebraic equations 
And find in the list Steady State
user should set diagram for which steady state should be found, form of the result (Diagram in steady state, Simulation result or Table with parameter values).
Additionally user may set which subset of Y variables will be used to check if steady state was found.
Example of analysis with parameters set is presented on fig. 2.
[[steady_state_analysis_example.png|thumb|Fig.2 Example of Steady State Analysis]]

@@ Line 4: / Line 4: @@
 In BioUML we have two analyses in that regard.
 <ol>
 <li>Algebraic steady state.
@@ Line 36: / Line 34: @@
 [[File:Steady_state_analysis_example.png|thumb|Fig.2 Example of Steady State Analysis]]
 </ol>

@@ Line 6: / Line 6: @@
-. Algebraic steady state.
+<ol>
 We transform the model to algebraic form<br> F(X, t)=0<br> and solve this algebraic system.
@@ Line 25: / Line 26: @@
 [[File:algebraic_steady_state_analysis_example.png|thumb|Fig.1 Example of Algebraic Steady State Analysis]]
-. Steady state.
+<li>Steady state.
 In this case we simply simulate the model from given initial values Y0 until Y stops changing in time.
@@ Line 34: / Line 35: @@
 Example of analysis with parameters set is presented on fig. 2.
 [[File:Steady_state_analysis_example.png|thumb|Fig.2 Example of Steady State Analysis]]

@@ Line 1: / Line 1: @@
 Steady state analysis of the mathematical model comprising system of ordinary differential equations <br>
 <center>dY/dt = f(X, t), Y(0) = Y0 </center>
-<br>implies finding X_SS and t such that f(X_SS, t) = 0, t > t_SS.<br>
+<br>implies finding X_SS and t_SS such that f(X_SS, t) = 0, t > t_SS.<br>
 In BioUML we have two analyses in that regard.

@@ Line 33: / Line 33: @@
 Additionally user may set which subset of Y variables will be used to check if steady state was found.
 Example of analysis with parameters set is presented on fig. 2.
-[[Fil:Steady_state_analysis_example.png|thumb|Fig.2 Example of Steady State Analysis]]
+[[File:Steady_state_analysis_example.png|thumb|Fig.2 Example of Steady State Analysis]]

@@ Line 23: / Line 23: @@
 User should set diagram for which steady state should be found and form of the result (table with parameter values or Simulation result).<br>
 Example of analysis with parameters set is presented on the Fig. 1.
-[[File::algebraic_steady_state_analysis_example.png|thumb|Fig.1 Example of Algebraic Steady State Analysis]]
+[[File:algebraic_steady_state_analysis_example.png|thumb|Fig.1 Example of Algebraic Steady State Analysis]]
 . Steady state.

@@ Line 21: / Line 21: @@
 In order to run Algebraic steady state analysis go to <b>Analysis</b> tab in the repository tree, select <b>Methods</b> then <b>Differential algebraic equations</b><br>
 The very first analysis in the list would be <b>Algebraic steady state analysis</b><br>.
-User should set diagram for which steady state should be found and form of the result (table with parameter values or Simulation result).
+User should set diagram for which steady state should be found and form of the result (table with parameter values or Simulation result).<br>
 Example of analysis with parameters set is presented on the Fig. 1.
 [[algebraic_steady_state_analysis_example.png|thumb|Fig.1 Example of Algebraic Steady State Analysis]]

Steady State Examples - Revision history

Axec@dote.ru at 11:09, 19 August 2021

Axec@dote.ru at 11:07, 19 August 2021

Axec@dote.ru at 11:06, 19 August 2021

Axec@dote.ru at 11:05, 19 August 2021

Axec@dote.ru at 11:05, 19 August 2021

Axec@dote.ru at 11:02, 19 August 2021

Axec@dote.ru at 11:02, 19 August 2021

Axec@dote.ru at 11:01, 19 August 2021

Axec@dote.ru: Created page with "Steady state analysis of the mathematical model comprising system of ordinary differential equations dY/dt = f(X, t), Y(0) = Y0 implies finding X_SS..."

Axec@dote.ru: Created page with "Steady state analysis of the mathematical model comprising system of ordinary differential equations
dY/dt = f(X, t), Y(0) = Y0
implies finding X_SS..."