Corporate Dynamics in Chains of Coupled Logistic Equations with Delay

The local dynamics of coupled chains of identical oscillators are considered. As a basic model of an oscillator, the well-known logistic equation with delay is proposed. The transition to studying a spatially distributed model is made. Two types of coupling of major interest are treated: diffusive coupling and unidirectional coupling. Critical cases are distinguished in the stability problem for the equilibrium state. It turns out that they are of infinite dimension: infinitely many roots of the characteristic equation tend to the imaginary axis as a small parameter characterizing the inverse of the number of elements in the chain tends to zero. The main result is the constructed special nonlinear boundary value problems whose nonlocal dynamics describes the behavior of all solutions for the chain in a neighborhood of the equilibrium state.