Derya Altıntan, Vilda Purutçuoğlu, Ömür Uğur, Impulsive Expressions in Stochastic Simulation Algorithms, International Journal of Computational Methods, 15(01), pp. 1750075, (February 2018).
Jumps can be seen in many natural processes. Classical deterministic modeling approach explains the dynamical behavior of such systems by using impulsive differential equations. This modeling strategy assumes that the dynamical behavior of the whole system is deterministic, continuous and it adds jumps to the state vector at certain times. Although deterministic approach is satisfactory in many cases, it is a well-known fact thatstochasticity or uncertainty has crucial importance for dynamical behavior of many others. In this study, we propose to include this abrupt change in the stochastic modeling approach, beside the deterministic one. In our model, we introduce jumps to chemical master equation and use the Gillespie direct method to simulate the evolutionary system. To illustrate the idea and distinguish the differences, we present some numerically solved examples.
Keywords: Stochastic Simulation Algorithm, Deterministic Approach, Impulsive Differential Equations, Stochastic Modeling, Chemical Master Equation, Direct Method