Towards possible q-generalizations of the Malthus and Verhulst growth models

Tsallis entropy introduced in 1988 based on the equation Sq=1−∑ipiqq−1 has been considered to obtain new possibilities for constructing a generalized thermodynamical basis for statistical physics, expanding classical Boltzmann–Gibbs thermodynamics for non-equilibrium states. During the last two decades this q-generalized theory has been successfully applied to a considerable amount of physically interesting complex phenomena. The authors wish to present a mathematical analysis of the possible q-generalizations of the Malthus and the Verhulst growth models based on Tsallis definitions of the q-logarithm and the q-exponential.