Simplified predator-prey reaction network.

Note: I'll use reaction networks rather than Petri nets. They are equivalent.

* \$$birth(\beta): rabbit \rightarrow rabbit + rabbit\$$

* \$$predation(\gamma): wolf + rabbit \rightarrow wolf + wolf\$$

* \$$death1(\rho): rabbit \rightarrow \$$

* \$$death2(\delta): wolf \rightarrow \$$

The values in parentheses are the transition rates.

The rate equations for these reactions are a system of nonlinear ODEs.

Let x(t) be the number of rabbits at time t, and y(t) be the number of wolves. Then:

* \$$x' = \beta x - \gamma x y - \rho x\$$

* \$$y' = \gamma x y - \delta y\$$