The stochastic reaction network in which chemical species evolve through a set of reactions is widely used to model processes physics, chemistry and biology. To characterize the evolving joint probability distribution state space counts requires solving system ordinary differential equations, master equation, where size counting increases exponentially with type species. This makes it challengi...

The study of the dynamics chemical reactions, and in particular unusual phenomena such as oscillation has led to development mathematical strategies for understanding equations governing their behavior. One feature this is recognition that dynamical properties a reaction can be predicted from graph theoretical certain network, called Chemical Reaction Network or CRN. It remarkable fact much the...

A new method to derive an essential integral kernel from any given reaction–diffusion network is proposed. Any describing metabolites or signals with arbitrary many factors can be reduced a single simpler system of integro-differential equations called “effective equation” including the (called kernel”) in convolution type. As one typical example, Mexican hat shaped theoretically derived two co...