Peter and Anti-Peter Principle as the Discrete Logistic Equation

In this work Peter principle (in the hierarchical structure any competent member tends to rise to his level of incompetence) is consistently interpreted as the discrete form of the well-known logistic (Verhulst or Maltusian) equation of the population dynamics. According to such interpretation anti-Peter principle (in the hierarchical structure any incompetent member tends to rise to his level of competence) is formulated too.