Simulation as a Method for Asymptotic System Behavior Identification (e.g. Water Frog Hemiclonal Population Systems)

Abstract

Studying any system requires development of ways to describe the variety of its conditions. Such development includes three steps. The first one is to identify groups of similar systems (associative typology). The second one is to identify groups of objects which are similar in characteristics important for their description (analytic typology). The third one is to arrange systems into groups based on their predicted common future (dynamic typology). We propose a method to build such a dynamic topology for a system. The first step is to build a simulation model of studied systems. The model must be undetermined and simulate stochastic processes. The model generates distribution of the studied systems output parameters with the same initial parameters. We prove the correctness of the model by aligning the parameters sets generated by the model with the set of the original systems conditions evaluated empirically. In case of a close match between the two, we can presume that the model is adequately describing the dynamics of the studied systems. On the next stage, we should determine the probability distribution of the systems transformation outcome. Such outcomes should be defined based on the simulation of the transformation of the systems during the time sufficient to determine its fate. If the systems demonstrate asymptotic behavior, its phase space can be divided into pools corresponding to its different future state prediction. A dynamic typology is determined by which of these pools each system falls into. We implemented the pipeline described above to study water frog hemiclonal population systems. Water frogs (Pelophylax esculentus complex) is an animal group displaying interspecific hybridization and non-mendelian inheritance.