Hongler, Max-Olivier2015-01-302015-01-302015-01-302015https://infoscience.epfl.ch/handle/20.500.14299/110694The cooperative dynamics of a 1-D collection of Markov jump, interacting stochastic processes is studied via a mean-field (MF) approach. In the time-asymptotic regime, the resulting nonlinear master equation is analytically solved. The nonlinearity compensates jumps induced diffusive behavior giving rise to a soliton-like stationary probability density. The soliton velocity and its sharpness both intimately depend on the interaction strength. Below a critical threshold of the strength of interactions, the cooperative behavior cannot be sustained leading to the destruction of the soliton-like solution. The bifurcation point for this behavioral phase transition is explicitly calculatedjump Markov processesexact solution of a nonlinear master equationmean-field description of interacting stochastic processessoliton-like propagating probability measures.text::journal::journal article::research article