Modelling the behaviour of a class of dynamical systems with Continuous Petri Nets

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 x_i is represented by a place p_i. When the derivative of a state x_i depends on positive or negative terms of x_i, then input or output transitions are added to p_i to represent the positive or negative terms respectively. If the derivative of x_i depends on positive terms of other state variable x_j then a transition going from p_j to p_i is added. If the derivative of x_i depends on negative terms of other state variable x_j, then a subnet removing the appropriate marking from p_i is added. In order to illustrate this methodology, we show how the well known chaotic Rossler system is translated into a TCPN.