A robustness approach to study metastable behaviours in a lattice-gas model of swarming

Abstract : Research in biology is increasingly interested in discrete dynamical systems to simulate natural phenomena with simple models. But how to take into account their robustness? We illustrate this issue by considering the behaviour of a lattice-gas model with an alignment-favouring interaction rule. This model, which has been shown to display a phase transition between an ordered and a disordered phase, follows ergodic dynamics. We present a method based on the study of stability and robustness, and show that the organised phase may result in several different behaviours. We then observe that behaviours are influenced asymptotically by the definition of the cellular lattice.