| Popis: |
This chapter focuses on periodic dynamics in autonomous Boolean networks. The goal is to design and characterize a periodic Boolean oscillator that can be coupled into networks to study the resulting network dynamics. The main challenge is to implement a coupling mechanism that is adjustable and can be tuned weak. In Sect. 6.1, I first introduce the existing theoretical and experimental work on periodic dynamical systems and their synchronization. Then, in Sect. 6.2, I show how periodic autonomous Boolean networks can be coupled in an “on”-“off” fashion in network motifs consisting of two periodic oscillators. In Sect. 6.3, I introduce and characterize a more advanced periodic Boolean oscillator that allows for weak coupling with adjustable coupling strength. I term this experimental periodic oscillator a Boolean phase oscillator because it bears resemblance to the Kuramoto model. Its coupling mechanism is characterized within network motifs (Results of this chapter are published in references Rosin et al. Chaos 23:025102, 2013; Phys Rev E 89:042907, 2014). The main contributions of this chapter are: (a) studying the dynamics of a simple periodic Boolean oscillator and small network motifs of this dynamical system; (b) designing, characterizing, and coupling of a periodic Boolean oscillator that allows for weak coupling; (c) developing models for the dynamical systems in this chapter. |
