Pithya
A Parallel Tool for Parameter Synthesis of Piecewise Multi-Affine Dynamical Systems
Nikola Beneš, Luboš Brim, Martin Demko, Samuel Pastva, David Šafránek
What is it that you do, anyway?
Two dimensional repressilator
Primitive biological switch: depending on the parameters,
either X or Y will dominate.
\frac{dX}{dt} = \mathbf{k} \cdot \frac{5^5}{5^5+Y^5} - 0.1 \cdot X
\frac{dY}{dt} = \frac{5^5}{5^5+X^5} - \mathbf{p} \cdot Y
Slides won't cut it? Try Pithya at pithya.ics.muni.cz
Autonomous ODE System
Piecewise Multi-affine ODE System
Autonomous ODE System
Abstract State Space
Property
HUCTL_P
Piecewise Multi-affine ODE System
Abstract State Space
Property
HUCTL_P
Coloured Model Checking
\begin{aligned}
stable & =\ \downarrow x : \mathbf{AG} \mathbf{EF} x \\
bistable & =\ stable \land \exists y \in stable : \neg \textbf{EF} y
\end{aligned}
Slides won't cut it? Try Pithya at pithya.ics.muni.cz
What's next?
Slides won't cut it? Try Pithya at pithya.ics.muni.cz
-
δ-decision based abstractions
- most current techniques are local and/or limited to specific types of equations
- Noise and/or environment input
Discrete Bifurcation Analysis
- Bifurcation points
- boundary points between parameter regions with equivalent behaviour
- Long term behaviour
Pithya
By Samuel Pastva
