Route to Chaos in Generalized Logistic Map

We postulate a generalization of well-known logistic map to open the possibility of optimization the modelling process of the population evolution. For proposed generalized equation we illustrate the character of the transition from regularity to chaos for the whole spectrum of model parameters. As an example we consider specific cases for both periodic and chaotic regime. We focus on the character of the corresponding bifurcation sequence and on the quantitative nature of the resulting attractor as well as its universal attribute (Feigenbaum constant).