Location: cellLib @ a7940fcacd45 / Components / MarkovS.cellml
- Author:
- WeiweiAi <wai484@aucklanduni.ac.nz>
- Date:
- 2023-04-04 15:51:18+12:00
- Desc:
- Add a steady state example
- Permanent Source URI:
- https://models.cellml.org/workspace/6bc/rawfile/a7940fcacd455a09bdb7beac0da91eca79cf1adb/Components/MarkovS.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- Markov states-->
<model name="MarkovS" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="units.cellml">
<units name="per_ms" units_ref="per_ms"/>
<units name="ms" units_ref="ms"/>
</import>
<!-- one connection-->
<component name="S1">
<variable name="t" public_interface="in" units="ms"/>
<variable name="Si_init" public_interface="in" units="dimensionless"/>
<variable name="k_i1" public_interface="in" units="per_ms"/>
<variable name="k_1i" public_interface="in" units="per_ms"/>
<variable name="norm" public_interface="in" units="dimensionless"/>
<variable name="S_1" public_interface="in" units="dimensionless"/>
<variable initial_value="Si_init" name="S_i" public_interface="out" units="dimensionless"/>
<variable name="dS_i" public_interface="out" units="per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>S_i</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_1i</ci>
<ci>S_1</ci>
</apply>
<ci>norm</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_i1</ci>
<ci>S_i</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dS_i</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_1i</ci>
<ci>S_1</ci>
</apply>
<ci>norm</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_i1</ci>
<ci>S_i</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- two connections-->
<component name="S2">
<variable name="t" public_interface="in" units="ms"/>
<variable name="Si_init" public_interface="in" units="dimensionless"/>
<variable name="k_i1" public_interface="in" units="per_ms"/>
<variable name="k_i2" public_interface="in" units="per_ms"/>
<variable name="k_1i" public_interface="in" units="per_ms"/>
<variable name="k_2i" public_interface="in" units="per_ms"/>
<variable name="norm" public_interface="in" units="dimensionless"/>
<variable name="S_1" public_interface="in" units="dimensionless"/>
<variable name="S_2" public_interface="in" units="dimensionless"/>
<variable initial_value="Si_init" name="S_i" public_interface="out" units="dimensionless"/>
<variable name="dS_i" public_interface="out" units="per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>S_i</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_1i</ci>
<ci>S_1</ci>
</apply>
<ci>norm</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_2i</ci>
<ci>S_2</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<ci>k_i1</ci>
<ci>k_i2</ci>
</apply>
<ci>S_i</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dS_i</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_1i</ci>
<ci>S_1</ci>
</apply>
<ci>norm</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_2i</ci>
<ci>S_2</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<ci>k_i1</ci>
<ci>k_i2</ci>
</apply>
<ci>S_i</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- three connections-->
<component name="S3">
<variable name="t" public_interface="in" units="ms"/>
<variable name="Si_init" public_interface="in" units="dimensionless"/>
<variable name="k_i1" public_interface="in" units="per_ms"/>
<variable name="k_i2" public_interface="in" units="per_ms"/>
<variable name="k_i3" public_interface="in" units="per_ms"/>
<variable name="k_1i" public_interface="in" units="per_ms"/>
<variable name="k_2i" public_interface="in" units="per_ms"/>
<variable name="k_3i" public_interface="in" units="per_ms"/>
<variable name="norm" public_interface="in" units="dimensionless"/>
<variable name="S_1" public_interface="in" units="dimensionless"/>
<variable name="S_2" public_interface="in" units="dimensionless"/>
<variable name="S_3" public_interface="in" units="dimensionless"/>
<variable initial_value="Si_init" name="S_i" public_interface="out" units="dimensionless"/>
<variable name="dS_i" public_interface="out" units="per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>S_i</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_1i</ci>
<ci>S_1</ci>
</apply>
<ci>norm</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_2i</ci>
<ci>S_2</ci>
</apply>
<ci>norm</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_3i</ci>
<ci>S_3</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<ci>k_i1</ci>
<ci>k_i2</ci>
<ci>k_i3</ci>
</apply>
<ci>S_i</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dS_i</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_1i</ci>
<ci>S_1</ci>
</apply>
<ci>norm</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_2i</ci>
<ci>S_2</ci>
</apply>
<ci>norm</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_3i</ci>
<ci>S_3</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<ci>k_i1</ci>
<ci>k_i2</ci>
<ci>k_i3</ci>
</apply>
<ci>S_i</ci>
</apply>
<ci>norm</ci>
</apply>
</apply>
</apply>
</math>
</component>
</model>