Some Properties And Dynamical Behaviors Of Complex Systems

In this thesis, we explor some properties and dynamical behaviors of complex systems. The main investigations are strange nonchaotic attractors in a time-delay system and some dynamical behaviors on complex networks. The studies in this thesis are as follows:First, We presented evidences of existence of strange nonchaotic attractors in a time-delay system. Compared with finite-dimensional systems described by ordinary differential equations, systems of delay differential equation (DDE) are infinite-dimensional. Thus, Our study extend the existence of strange nonchaotic attractors from finite-dimensional systems to infinite-dimensional systems. Strange nonchaotic attractors can be realized not only in quasiperiodically driven systems,autonomous discrete-time maps and periodically driven continuous-time systems but also in systems of delay differential equation (DDE).In the second, with the aim to enhance the transport capacity of scale-free networks, we studied the relation between the degree correlation and the transport capacity of the network. We calculated degree-degree correlation coefficient, maximal betweenness and critical value of generating rate Rc (for R> Rc traffic congestion occurs). Numerical experiments indicate that assortative mixing and disassortative mixing can both enhance the transport capacity. We also reveal how the topological structure affects the transport capacity of the network. Assortative (disassortative) mixing changes the distributions of node betweennesses, as a result, the traffic through the nodes with highest degrees decreases and the traffic through the initially idle nodes increases.Thirdly, considering the fact in real worlds that information transmits with time delay, we studied an evolutionary spatial prisoner's dilemma game where agents update strategies according to certain information they learned. In our study, the game dynamics is classified from the modes of information learning as well as game interaction, and four different com-binations, i.e., the mean-field case, case I, case II, and local case are studied comparatively. It is found that time delay in case II smoothes the phase transition from the absorbing states of C (or D) to their mixing state, and promotes cooperation for most parameter values. These are shown on both regular rings and square lattices. Our work provides insights into the temporal behavior of information and the memory of the system, and may be helpful in understanding the cooperative behavior induced by the time delay in social and biological systems.Finally, we studied four-state rock-paper-scissors games on unfixed networks. Initially, each node of the square lattice either keep empty or can be occupied by an individual whose state can be A, B, or C. At each time step, a stochastic long-range connection is temporarily appended with probability p to the individual which will interact with its neighbors. Time evolution of the densities of species and pattern formation are investigated by Monte Carlo simulations and the analysis of the stochastic partial differential equations. Similar cyclical changes of the densities of three species are observed over a wide range of p values. Numerical solutions of stochastic partial differential equations coincide well with the simulations on unfixed networks. Biodiversity vanishes when p larger than a certain value, In the vicinity of the transition point, MC data simulated by smaller interval of p can be well approximated by a power law behaviour (1-Pext)～P-γ(Pext is the extinction probability). It is also found that there may be a critical value p'c in the region about (0.47,0.58), when p> p'c the biodiversity is extinct in the system of any size.