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Biology — Petri Net: Predator-Prey

A token model of the Lotka-Volterra dynamics.

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Predator-prey dynamicsw=2w=2Preyω unboundedPredatorsω unboundedPrey reproduceenabledPredationenabledPredator deathenabledReachable markings—unbounded — no finite setTerminates—not decidedLive transitions—not decidedSafe places0/22 unboundedConservation laws02 places in none2 places unbounded, so this net has no finite reachable set.`birth -> Prey` is written 2 times. The weights ADD, so the pair moves 2 tokens per firing — which is exactly what a Petri net means by repeated arcs, and how a stoichiometric coefficient is writte…`predation -> Predator` is written 2 times. The weights ADD, so the pair moves 2 tokens per firing — which is exactly what a Petri net means by repeated arcs, and how a stoichiometric coefficient i…Place `Prey` is UNBOUNDED: there is a firing sequence that raises its token count and it can be repeated for ever, so this net puts no upper bound on what the place holds. That is a proof from the …Place `Predators` is UNBOUNDED: there is a firing sequence that raises its token count and it can be repeated for ever, so this net puts no upper bound on what the place holds. That is a proof from…2 places are weighted by no conservation law — `Prey`, `Predators`. Nothing in the structure of this net holds what they hold constant, so their token count is free to drift with the firing sequenc…

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title Predator-prey dynamics

place Prey tokens 4 "Prey"
place Predator tokens 2 "Predators"
transition birth "Prey reproduce"
transition predation "Predation"
transition death "Predator death"

Prey -> birth
birth -> Prey
birth -> Prey
Prey -> predation
Predator -> predation
predation -> Predator
predation -> Predator
Predator -> death