Time Reversal of the Increasing Geometrical Progression of the   Population of a Simple Biological Specie
  In this work we consider time reversal of the increasing geometrical progression of the population of a simple biological species without any enemies (predators) in the appropriate environment with unlimited resources (food, territory, etc.). It is shown that such time reversal corresponds to appearance of the cannibalism, i.e. self-predaciousness or self-damping phenomena which can be described by a type of difference Verhulst equation. 
Vladan Pankovic, Rade Glavatovic and Milan Predojevic