A framework for modeling information propagation of biological systems at critical states

We explore the dynamics of information propagation at the critical state of a biologically inspired system by an individual-based computer model. "Quorum response", a type of social interaction which has been recognized taxonomically in animal groups, is applied as the sole interaction rule among individuals. In the model, we assume a truncated Gaussian distribution to depict the distribution of the individuals' vigilance level. Each individual can assume either a naïve state or an alarmed one and only switches from the former state to the latter one. If an individual has turned into an alarmed state, it stays in the state during the process of information propagation. Initially, each individual is set to be at the naïve state and information is tapped into the system by perturbing an individual at the boundaries (alerting it to the alarmed state). The system evolves as individuals turn into the alarmed state, according to the quorum response rules, consecutively. We find that by fine-tuning the parameters of the mean and the standard deviation of the Gaussian distribution, the system is poised at a critical state. We present the phase diagrams to exhibit that the parameter space is divided into a super-critical and a sub-critical zone, in which the dynamics of information propagation varies largely. We then investigate the effects of the individuals' mobility on the critical state, and allow a proportion of randomly chosen individuals to exchange their positions at each time step. We find that mobility breaks down criticality of the system.