One of the main question in clinical medicine is how to stabilize the patient. In the fact of the oscillating heart, breathing, circadian rhythm or menstruation cycle the model could be designed as non-oscillating with variables such as period times, amplitudes, frequencies, mean values and other phase space variables. This type of model has better numerical stability for longer simulation time and even more it can be "stabilized". This stabilization we called steady state.

To be mathematically exact, we define an * steady state
system* (SSS) as a non-differential system derived from a
original differential system (DS) by using zero derivations and by
adding

Adding of one ASSE is possible by inserting and connecting of the energy or mass conservation law block from package SteadyState.Components. Other possibilities is in blocks of environment sources, where the setting of parameter isIsolatedInSteadyState add the equation of the zero mass/volume/energy flow from or to environment.

The model in steady state often changes to one big nonlinear strong component, but without solver stiff or convergence problems. Especially in quick chemical reaction kinetics is not necessary to have very rapid molar fluxes, when it always reach equilibrium. This design also approve to create steady stated parts in dynamical model without huge rebuilding. It also brings other benefits. To see these possibilities, one have to realize that conservation laws could be invariances in a dynamical simulation. This is really useful for debugging.

It is always a big challenge to nicely solve initial values of differential system. However, it should be possible to solve the SSS in initial phase. And this is the idea behind the Types.SimulationTypes.InitSteadyState option for models already extended with ASSE to support SSS.

Name | Description |
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Examples | Examples that demonstrate usage of the Pressure flow components |

Components | |

Interfaces |

Copyright (c) 2008-2015, Marek Mateják, Charles University in Prague

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