Understanding the cooperation-competition dynamics is a long-standing challenge in studying complex systems.Inspired by the idea of Shannon entropy, we define competition information entropy and propose an entropy evo...Understanding the cooperation-competition dynamics is a long-standing challenge in studying complex systems.Inspired by the idea of Shannon entropy, we define competition information entropy and propose an entropy evolution model. The analytic results of the model of the relation between competition gain distribution parameters and entropy, as well as the relation between entropy and time are compared with empirical results obtained in 14 real world systems. They are found to be in good agreement with each other.展开更多
As an research example of the widely existing cooperation-competition systems,the authorspresent an empirical investigation on a fruit nutritive factor network.It is described by a node-weightedbipartite graph.The fru...As an research example of the widely existing cooperation-competition systems,the authorspresent an empirical investigation on a fruit nutritive factor network.It is described by a node-weightedbipartite graph.The fruit nutritive factors are defined as the nodes,and two nodes are connected by anedge if at least one fruit contains these two nutritive factors.The fruits are defined as the collaborationacts.The node-weight W_(nt),which signifies the 'importance degree' of each actor node,is defined as thecont ent of a nutritive factor in a fruit.The empirical investigation results show some unique features.The node-weight distributions take so-called 'shifted power law' function forms,but the act-weightdistribution takes a normal form.The degree and act-degree distributions show impulsive-spectrumlike forms.These observations may be helpful for the study of fruits.The network description methodproposed in this article may be universal for a kind of cooperation-competition systems.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10635040 and 70671089)
文摘Understanding the cooperation-competition dynamics is a long-standing challenge in studying complex systems.Inspired by the idea of Shannon entropy, we define competition information entropy and propose an entropy evolution model. The analytic results of the model of the relation between competition gain distribution parameters and entropy, as well as the relation between entropy and time are compared with empirical results obtained in 14 real world systems. They are found to be in good agreement with each other.
基金supported by the National Natural Science Foundation of China under Grant Nos. 10635040 and 70671089
文摘As an research example of the widely existing cooperation-competition systems,the authorspresent an empirical investigation on a fruit nutritive factor network.It is described by a node-weightedbipartite graph.The fruit nutritive factors are defined as the nodes,and two nodes are connected by anedge if at least one fruit contains these two nutritive factors.The fruits are defined as the collaborationacts.The node-weight W_(nt),which signifies the 'importance degree' of each actor node,is defined as thecont ent of a nutritive factor in a fruit.The empirical investigation results show some unique features.The node-weight distributions take so-called 'shifted power law' function forms,but the act-weightdistribution takes a normal form.The degree and act-degree distributions show impulsive-spectrumlike forms.These observations may be helpful for the study of fruits.The network description methodproposed in this article may be universal for a kind of cooperation-competition systems.
