The Research Of Estimating The Varying Topology Of Discrete-Time Complex Dynamical Networks

The study of complex dynamical networks has rapidly been attracting interest within the natural and social sciences. A complex dynamical network can be considered a graph where each node is a dynamical system connected to other dynamical systems through signal coupling. The connection topology plays an essential role in the cooperative behavior of networks. However, estimating the topology of complex dynamical network has not been fully investigated. Most of the existing methods make the assumption that the exact topology of the underlying network is invariable, and are only applied to estimate the topology of continuous-time dynamical networks. Meanwhile many real-world networks have varying topology, such as in the case that new nodes enter the network with time, and the available data are usually in discrete-time format in practical applications. Additionally, noise usually deteriorates the performance of parameter estimation, and leads to fluctuation of the estimates around true values in practice. However, less attention has been given to this point in previous research. In this thesis, how to estimate the varying topology of discrete-time dynamical networks with noise has been analyzed. The main results are as follows:1、Designing an appropriate network estimator to estimate the varying-topology of discrete-time dynamical networks based on autosynchronization: first, systematically analyzing topological estimation in theory; then, obtaining the optimum parameter for convergence; last, simulating several illustrative examples of application, including a 3D hyperchaotic R?ssler discrete-time dynamical network and some larger SW small-world networks and BA scale-free networks. Especially, Our method provides a general tool for topology estimation of discrete-time dynamical networks(weighted or unweighted, directed or undirected, and possibly nonuniform dynamics of each node). Numerical simulations present the iteration steps of this method is less than the existing methods, i.e. this method converges more quickly than the existing methods.2、Proposing to use the moving-average filter to suppress the effect of noise in experimental outputs. The simulations of the performances of the above networks with and without noise demonstrate that using the moving-average filter the estimated value is closer real value.3、Applying this method to estimate the topology of the gene regular network. Obtaining the topology and dynamics of gene regulatory network, and even predicting or controlling its expression is a major challenge in life science. The complete flow includes four steps(Preparation, Cubic spline interpolation, Curve fitting and Topology estimation). Although this method only needs the expression rate of a small number of sample time points, it could obtain the transcription rate of the target gene and predict the expression profile of the next cell cycle under the same condition or predict the expression profile in the interval between two sample time points or predict the deficiency data.