This paper is devoted to the study of global asymptotic behavior in some cooperative systems of functional differential equations. We first prove a general global result for both discrete-time and continuous dynamical systems on the subset of a strongly ordered Banach space. Then we discuss cooperative systems of functional differential equations and further obtain a threshold theorem on their ...

The 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 bo...