One of the major problems in dealing with interacting finite populations of agents, such as molecules in chemistry or people in populations, is that there always exists a probability of one species or state going extinct. Predicting the probability of extinction requires a knowledge of how the dynamics progresses towards extinction. The path that optimizes the probability to extinction is defined to be the optimal path. Here we present an ...
Real networks consisting of social contacts do not possess static connections. That is, social connections may be time dependent due to a variety of individual behavioral decisions based on current network connections. Examples of adaptive networks occur in epidemics, where information about infectious individuals may change the rewiring of healthy people, or in the recruitment of individuals to a cause or fad, where rewiring may optimize recruitment of susceptible individuals. ...
Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We ...
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