Title: Feedback induced stationary and oscillatory patterns in complex bistable networks
Abstract: In this talk we will present theoretical and experimental findings on pattern formation in bistable chemical networks. Effects of feedbacks on self-organization phenomena will also be discussed. For regular trees, an approximate analytical theory for localized stationary patterns under application of global feedbacks is constructed. Using it, properties of such patterns in different parts of the parameter space are discussed. We will also show that localized oscillatory patterns can be formed in these networks if the global feedback is applied with certain time delay. Linear stability analysis has revealed a critical time delay for which the system undergoes a Hopf bifurcation and exhibits limit cycles of small amplitudes. Furthermore, we will present results from numerical investigations for large random Erdös-Rényi and scale-free networks. In both kinds of systems localized active patterns consist of a subnetwork, whose size decreases as the feedback intensity increases. In the later random networks local feedbacks affecting only the hubs or the peripheral nodes are also considered.