Numerical simulation of Verhulst-type kinetics with Poisson white noise

A new numerical method is developed for finding response samples for a Verhulst-type system subjected to Poisson white noise. The method based on the three following steps: first, zero-one jump law was used to generate the sample paths of Poisson white noise, which worked as the system inputs, then the classical Heun method was used to calculate the system outputs corresponding to the generated input samples, and last we estimated the response statistics from repeating sample outputs by previous steps. The accuracy and efficiency of the proposed method are examined by Verhulst-type systems driven by Poisson white noise.