Modelling the behaviour of a class of dynamical systems with Continuous Petri Nets
Manuel Navarro‐Gutiérrez, Antonio Ramírez‐Treviño, David Gómez‐Gutiérrez · 2013
This work is concerned with the problem of translating an ordinary differential equation (ODE) with an attractor into a Timed Continuous Petri Net (TCPN) with product semantics. The proposed translation methodology starts by shifting the ODE attractor to a suitable value such that the system evolution is confined to the first orthant (i.e. the evolution will be positive). In the proposed methodology, a state xiis represented by a place pi. When the derivative of a state xidepends on positive or negative terms of xi, then input or output transitions are added to pito represent the positive or negative terms respectively. If the derivative of xidepends on positive terms of other state variable xjthen a transition going from pjto piis added. If the derivative of xidepends on negative terms of other state variable xj, then a subnet removing the appropriate marking from piis added. In order to illustrate this methodology, we show how the well known chaotic Rossler system is translated into a TCPN.