> Autonomous versus non-autonomous equations. Lotka-Volterra belongs to the former category, a time-invariant system -- is that a stretch for describing real systems where populations depend on the environment? What good will that behavioral description do when the prey species is susceptible to e.g. drought cycles?
We can get a richer model for Petri nets if we allow the rate coefficients to vary with time. Then we could build a Petri net model with processes like reproduction of prey, death of prey, predation, and death of predators. By allowing the processes for death-of-prey and death-of-predators to have time-dependent rate coefficients, external driving forces like the effects of droughts can be expressed.
In this way, the structure of the network will capture some aspects of the dynamics, but not all. It could be coupled with other models or data for the external factors.
Note this is not a full leap to the generality of non-autonomous equations, as the rate equations are still _derived_ from a network structure and the assumptions about its dynamics. This will of course lead to non-autonomous rate equations - but only to a specific subset of them.