Qualitative Analysis Of Two Types Of Network Models

In recent years, the rise of complex network researchers makes people begin to pay attention tothe complexity of the network structures and the relationships between the network behaviors. Tounderstand the relationships and to improve the behaviors of the network, people need to have a goodknowledge of the structure characteristics of actual network. Based on this, a suitable networkstructure model could be established. Nowadays, a lot of extensive empirical studies have beenconducted in many different areas. Plankton system as a kind of ecological complex network, thestudy of it has not only environmental protection significance, but also has economic meaning.Another closely related with human network model---neural network model has also beensuccessfully applied to various fields of human life, the study of it has important practical significance.On the basis of analysis and summary of research status of delay reaction-diffusion planktoneconomic networks and the neural network, employing stability, bifurcation and Turing’s theory, theauthor studies the dynamical behaviors of the above two network models. The paper is organized asfollows:In the first Chapter, the author elaborates the delay reaction-diffusion plankton economic systemwith harvest control, differential algebraic plankton ecomic system and reaction-diffusion neuralnetwork model. The main content of this paper is expounded.The second Chapter establishes a delay reaction-diffusion plankton economic network modelwith harvesting control and discusses the stability and bifurcation problems of the system. Selectingdelay as the bifurcation parameter, the local asymptotic stability and Hopf bifurcation of zero balance,boundary point and the positive equilibrium point of system are studied.The third Chapter studies the locally asymptotic stability of equilibria of ecological economicsystem when ecological balance happens. And, the stability of positive equilibrium point andbifurcation problems is also considered.The forth Chapter talks about the Turing unstability of reaction-diffusion neural network anddecuces the coefficients of amplitude equation and considers Turing pattern selection and stability.The fifth Chapter summarizes the rearch work of this dissertation. Furthermore, the futureresearch direction is made.