5.1.3.4. Example: Cascading

Description: Because resets change the value of variables, they can also trigger downstream reset activity as conditions which were not previously met become active.

Note that:

• all elements are in the same component;

• the order values of resets are not shown; and

• all variables have dimensionless units.

component:
  ├─ math:
  │   ├─ ode(A, t) = 1
  │   └─ ode(B, t) = 1
  │
  ├─ variable: A initially 1
  │    └─ reset: rule 1
  │        ├─ when A == 4
  │        └─ then B = 5
  │
  └─ variable: B initially 2
       └─ reset: rule 2
           ├─ when A == 5
           └─ then B = 6

See CellML syntax

<variable name="t" units="dimensionless" />
<variable name="A" units="dimensionless" initial_value="1" />
<variable name="B" units="dimensionless" initial_value="2" />

<math>
    <apply><eq/>
        <diff>
            <ci>A</ci>
            <bvar>t</bvar>
        </diff>
        <cn cellml:units="dimensionless">1</cn>
    </apply>
</math>

<math>
    <apply><eq/>
        <diff>
            <ci>B</ci>
            <bvar>t</bvar>
        </diff>
        <cn cellml:units="dimensionless">1</cn>
    </apply>
</math>

<!-- Reset rule 1: -->
<reset variable="A" test_variable="B">
    <test_value>
        <cn units="cellml:dimensionless">4</cn>
    </test_value>
    <reset_value>
        <cn units="cellml:dimensionless">5</cn>
    </reset_value>
</reset>

<!-- Reset rule 2: -->
<reset variable="B" test_variable="A">
    <test_value>
        <cn units="cellml:dimensionless">5</cn>
    </test_value>
    <reset_value>
        <cn units="cellml:dimensionless">6</cn>
    </reset_value>
</reset>

At t = 2 the following situation occurs:

t	0	1	2
A	1	2	3
B	2	3	4

At this point reset rule 1 is the only active reset. The change is applied:

t	0	1	2
A	1	2	3 → 5
B	2	3	4

Because the new point differs from the last, a second cycle of reset rule checking is started. In this cycle, only reset rule 2 is active. Again, the change is applied:

t	0	1	2
A	1	2	3 → 5
B	2	3	4 → 6

A third cycle is started, in which B is still active, but after applying the updates the new point is the same as at the end of cycle two, so reset evaluations halts and model dynamics continue.

t	0	1	2	3	…
A	1	2	3 → 5	6	…
B	2	3	4 → 6	7	…