Abstract
Mathematical modeling is playing a very important role in clarifying, analyzing, and drawing of qualitative and quantitative results. In almost every area of sciences, the complex system is being modeled using some mathematical modeling using a graphical approach, differential equation approach, statistical approach, and many more. In this chapter, we are focusing on the graphical approach using Petri Nets (PN). Petri net came in focus in the early ‘90s after Carl Adam introduced this method in his Ph.D. thesis. By then, it is being widely used to model the complex systems in engineering, computational, biological, and many more fields. Initially, it was accounted as a modeling tool in Computer Science (CS), but later, PN method started to model systems in Automatic Control (AC) too for automation after that it was being used in the background of Operations Research (OR). Therefore, this method recognized as the Discrete Event Dynamic Systems (DEDS) theory, at the intersection of CS, AC, and OR. Moreover, different kinds of hybrid PNs like Time Petri Net (TPN), Stochastic Petri Net (SPN) are being extensively studied today. PN is also being proved to be a useful tool to model the biological system like cell cycle, pathways in diseases to treat, and many more. It will help to find several structural and behavioral properties of the system.
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