Epidemic Spreading Model Based on Social Active Degree in Social Networks

In this paper,an improved Susceptible-Infected-Susceptible(SIS) epidemic spreading model is proposed in order to provide a theoretical method to analyze and predict the spreading of diseases.This model is based on the following ideas:in social networks,the contact probability between nodes is decided by their social distances and their active degrees.The contact probability of two indirectly connected nodes is decided by the shortest path between them.Theoretical analysis and simulation experiment were conducted to evaluate the performance of this improved model.Because the proposed model is independent of the network structure,simulation experiments were done in several kinds of networks,namely the ER network,the random regular network,the WS small world network,and the BA scale-free network,in order to study the influences of certain factors have on the epidemic spreading,such as the social contact active degree,the network structure,the average degree,etc.This improved model provides an idea for studying the spreading rule of computer virus,attitudes,fashion styles and public opinions in social networks.

Bifurcation control and eigenstructure assignment in continuous solution polymerization of vinyl acetate

The major difficulty in achieving good performance of industrial polymerization reactors lies in the lack of understanding of their nonlinear dynamics and the lack of well-developed techniques for the control of nonlinear processes, which are usually accompanied with bifurcation phenomenon. This work aims at investigating the nonlinear behavior of the parameterized nonlinear system of vinyl acetate polymerization and further modifying the bifurcation characteristics of this process via a washout filter-aid controller, with all the original steady state equilibria preserved. Advantages and possible extensions of the proposed methodology are discussed to provide scientific guide for further controller design and operation improvement.

RQI DYNAMICS FOR NON-NORMAL MATRICES WITHREAL EIGENVALUES

RQI is an approach for eigenvectors of matrices. In 1974, B.N Parlett proved that it was a ''succeessful algorithm'' with cubic convergent speed for normal matrices. After then, several authors developed relevant theory and put this research into dynamical frame. [3] indicated that RQI failed for non-normal matrices with complex eigenvalues. In this paper, RQI for non-normal matrices with only real spectrum is analyzed. The authors proved that eigenvectors are super-attractive fixed points of RQI. The geometrical and topological behaviours of two periodic orbits are considered too. The existness of three or higher periodic orbits and their geometry are considered too. The existness of three or higher periodic orbits and their geometry are still open and of interest. It will be reported in our forthcomming paper.