Fractional-order singular logistic map: Stability, bifurcation and chaos analysis

Recently fractional calculus started to gain much importance due to its applications to the mathematical modeling of real phenomena with memory effect. Besides, singular modeling, which has been accompanied by exhibiting more complicated dynamics rather than standard models, can reveal the instability mechanism of wide-range of physical systems. Utilizing these two applicable techniques of modeling, a generalization of the logistic growth model, which takes into account the effects of memory and economic interest, is suggested in this paper. Besides mathematical analysis and extracting new results on the equilibrium points and local stability studies of discrete-time commensurate fractional-order singular (FOS) state space systems, some basic dynamical properties and qualitative analysis of the new chaotic FOS logistic map are studied, either numerically or analytically, to explore the impacts of real order and economic interest on the presented system in biological contexts. (C) 2018 Elsevier Ltd. All rights reserved.