Abstract
Boolean networks play an important role in modern biology as popular alternatives to traditional continuous models. After a brief introduction, we will analyze two main features that influence the dynamics: network topology and the Boolean functions. Of particular interest are the canalizing functions, which model a biological robustness concept proposed by geneticist C.H. Waddington in 1942. After an in-depth look at canalizing functions, we will conclude with an analysis of the stability of Boolean network dynamics. Loosely speaking, Boolean networks fall into one of two dynamical regimes, ordered and critical, which are characterized by whether small perturbations tend to die out or propagate through the network. These regimes are separated by the narrow critical threshold, where many real-world networks are believed to lie. Critical networks optimize the trade-off of being robust enough to withstand external perturbations yet flexible enough to exhibit complex dynamics and evolve.
Published Version
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