Organizing principles and dynamics of complex networks

Abstract

Evolution has shaped all living organisms, and It is the strongest organizing principle. Robustness and efficiency are its consequences. Another strange outcome of the evolution is a society. Selfish genes behave altruistically and form societies. This dissertation focuses on the robustness, efficiency, and society of living organisms. $\textbf{Robustness}$ Most researches adopted discrete-time, synchronously updated Kauffman network model in studying the genetic network, although the time evolution of genes is not synchronous. The effect of synchronous update has not yet been fully revealed. To measure the robustness of the dynamics against asynchronousity of update in detail, a method, similar to non-equilibrium kinetic Ising model, is suggested. It can vary the synchronousity of update continuously. In the simulation of the yeast??? cell cycle network, it is found that the asynchronousity damages the robustness of the dynamics quickly, i.e. the robustness of the biological pathway decreases exponentially as the asynchronousity increases. Most real-world (scale-free) networks have in-homogeneous degree distribution and thus are robust against random error, but fragile against targeted attack. By the same origin, the scale-free networks are vulnerable to epidemic spreading. We investigate the epidemic dynamics of two interacting species~($A$ and $B$) with asymmetrical coupling on scale-free networks. The coupling between the species is asymmetric; $A$ induces $B$ while $B$ kills $A$. This model is inspired by the immune system of living organisms and the worm-killer worm in the Internet. A particle $A$ branches according to the susceptible-infected-susceptible~(SIS) model. However, we adopt the less-reproductive the contact process~(CP) dynamics for the particle $B$ since it would be costly to activate an immnune system in real systems and we do not want to flood the network with the $B$ particles. Our model in SF networks shows much richer proper...