Linking the Pattern Structures to System Robustness Based on Dynamical Models and Statistical Method

Pattern structures are usually used to describe the spatial and temporal distribution characteristics of individuals. However, the corresponding relationship between the pattern structure and system robustness is not well understood. In this work, we use geostatistical method–semivariogram to study system robustness for different pattern structures based on three dynamical models in different fields. The results show that the structural ratio of different pattern structures including the mixed state of spot and stripe, cold spot, stripe only, and hot spot are more than 75%, which indicated those patterns all have strong spatial dependence and heterogeneity. It was revealed that the systems corresponding to the mixed state of spot and stripe or cold spot are more robust. This article proposed a method to characterize the robustness of the system corresponding to the pattern structure and also provided a feasible approach for the study of “how structures determine their functions.”