Control, Dynamics, and Epidemic Spreading in Complex Systems

Abstract

In this thesis we investigate three problems involving the control and dynamics of complex systems. (a) We first address the problem of controlling spatiotemporally chaotic systems using a forecast-based feedback control technique. As an example, we suppress turbulent spikes in simulations of the two-dimensional complex Ginzburg-Landau equation in the limit of small dissipation. (b) In our second problem we examine the dynamical evolution of the one-dimensional self-organized forest fire model, when the system is far from its statistically steady-state. In particular, we investigate situations in which conditions change on a time-scale that is faster than, or of the order of the typical system relaxation time. (c) Finally, we provide a mean field theory for a discrete time-step model of epidemic spreading on uncorrelated networks. The effect of degree distribution, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations.