The age model of  cellular communities is considered.
Delay-differential equations and their model systems for cellular
communities are constructed and quantitatively analyzed. It is
determined that there are the following states: rest, stationary
state, Poincar\'{e} type limit cycles, dynamic chaos and \lq\lq black hole\rq\rq\
effect. Regularities for the origin of dynamic chaos, \lq\lq r-windows\rq\rq\ 
regions and prediction problems for the determination of destructive
changes - \lq\lq black hole\rq\rq\ effect, are investigated. The results of the
developed approaches are applied to the quantitative analysis of
cellular communities and the delay-differential equations of
animal and plant organisms are considered.