We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve towards a chosen attractor, for example initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groeb...

There are many methods for solving a nonlinear algebraic equation. The methods are classified by the order, informational efficiency and efficiency index. Here we consider other criteria, namely the basin of attraction of the method and its dependence on the order. We discuss several third and fourth order methods to find simple zeros. The relationship between the basins of attraction and the c...

Until now, several methods have been developed to compute the domains of attraction for stationary points of polynomial non-linear systems. For the case of non-polynomial systems, though, this question is still open. In this paper a new method, based on Lyapunov’s stability theory and the theorem of Ehlich and Zeller, is presented for the computation of domains of attraction of non-polynomial s...

The goal of this work is to enhance Internet security by applying formal analysis of traffic attraction attacks on the BGP routing protocol. BGP is the sole protocol used throughout the Internet for interdomain routing, hence its importance. In attraction attacks an attacker sends false routing advertisements to gain attraction of extra traffic in order to increase its revenue from customers, d...