An Inverse Voter Model For Co-evolutionary Networks And A Model For Food Webs

In this thesis, we investigate an inverse voter model for co-evolutionary networks and a model for food webs.In the first chapter, we introduce the basic concepts and backgrounds of the thesis. In the second chapter, starting from Ising model, and usingρ+- as the density of“+-”links as the efficiency of flow produced in networks, we study the evolution effects on a static network with binary state nodes with four different strategies. With comparison, network can get a higher efficiency with global information on each node. Meanwhile, fixed long range order goes against the improvement of efficiency.In a sort of co-evolutionary networks, nodes always flip their states between two opposite ones, changing the types of links to their nearest neighbors correspondingly. Meanwhile, link rewiring and binary state flipping feed back with each other in a dynamic process, and only links between nodes in opposite states are productive in generating flow for the network. In the third chapter, we propose an inverse voter model to depict basic features of them. An order parameter complementary to the flow-producing efficiency is defined to describe a new phase transition for the co-evolution starting from random graphs or small-world networks. We obtain a phase border separating full efficient from deficient behaviors analytically with mean-field approximation, and get scaling relations of the order parameter versus independent variables (β,?k) which are normalized inverse temperature and average degree, respectively, by simulations. With the model we advocate to describe the efficiency of a network pertaining to its function, node states and link properties related with it. Sparseness of flow networks is revisited from the viewpoint of efficiency. In inverse voter model, there are also numerical evidences indicating the existence of self-organized criticality and least action principle in co-evolutionary complex networks.In the fourth chapter, based on competitive exclusion principle in ecology, and assuming the trophic level s inversely proportional to the population N of species, we set up a co-evolutionary food web model with simple prey-predator relationship. With co-evolutionary process in food web, 13 numerical results can be worked out and fit well with the results of field observations (totally 16).