The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful However, wh...The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful However, what are the su^cient and necessary conditions of the existence of the potential function is still an open problem. Use Hodge decomposition theorem in differential form theory, we focus on the general chemical Langevin equations, which reitect complex chemical reaction systems. We analysis the conditions for the existence of potential landscape of the systems. By mapping the stochastic differential equations to a Hamiltonian mechanical system, we obtain the Fokker-Planck equation of the chemical reaction systems. The obtained Fokker-Planck equation can be used in further studies of other steady properties of complex chemical reaction systems, such as their steady state entropies.展开更多
基金Supported in part by the National Basic Research Program of China(973 Program)under Grants No.2007CB935903the National Nature Science Foundation of China under Grant No.11074259
文摘The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful However, what are the su^cient and necessary conditions of the existence of the potential function is still an open problem. Use Hodge decomposition theorem in differential form theory, we focus on the general chemical Langevin equations, which reitect complex chemical reaction systems. We analysis the conditions for the existence of potential landscape of the systems. By mapping the stochastic differential equations to a Hamiltonian mechanical system, we obtain the Fokker-Planck equation of the chemical reaction systems. The obtained Fokker-Planck equation can be used in further studies of other steady properties of complex chemical reaction systems, such as their steady state entropies.
