In this paper, we consider an AK model augmented with a productive externality of nature and a process of natural capital accumulation where a reproduction force is moderated by the negative impact of productive pollution. Differently from the existing literature, more focused on the planner's solution, we consider a market economy and the effects of its imperfections. We introduce two distinct natural accumulation processes: a power law, more usual in economics, and a logistic law, more popular in ecology. In both cases, we observe the occurrence of cycles of period two, cycle of period a power of two and chaos through a flip bifurcation and perioddoubling bifurcations. In the case of the power law, dynamics are even richer because of the possibility of limit cycles through a Neimark-Sacker bifurcation. In the case of a power law, cycles occur under a larger Total Factor Productivity because the TFP amplifies the negative impact of pollution on natural regeneration. In the case of a logistic law, cycles take place when the saturation effect of nature as a larger negative impact on the reproduction process.