Complex attractors and basins in a growth model with nonconcave production function and logistic population growth rate

In this paper we study a discrete-time growth model of the Solow type with nonconcave production function where shareholders save more than workers and the population growth dynamics is described by the logistic equation. We prove that the resulting system has a compact global attractor and we describe its structure. We also perform a mainly numerical analysis to show that complex features are exhibited, related both to the structure of the coexisting attractors and to their basins. The study presented aims at showing the existence of complex dynamics when the elasticity of substitution between production factors is not too high (so that capital income declines) or the parameter in the logistic equation increases (so that the amplitude of movements in the population growth rate increases).