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The goal of this paper is to review some of the works on the dynamics of economic models in which the environmental variable is introduced. In particular, we will focus on models that in addition to giving some analytical insights into the coevolution of economic and environmental systems, they can give rise to nonlinear dynamic effects as the emergence of chaotic dynamics, multistability and (local and global) indeterminacy. However, several questions on this issue remain open and we hope that our paper may attract researchers to contribute to this topic.

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In the present work, we analyze the emergence of fashion cycles and complex phenomena in a discrete time dynamic model in which a population is divided into two groups, bandwagoners and snobs. Both groups react differently to the aggregate demand for goods in the previous period and, in particular, bandwagoners imitate the consumption styles prevailing in society, while snobs try to distinguish themselves from them. We consider a first specification of the model in which the structure of the population is fixed and we show how in the case of polymorphic population it is possible to observe cyclical behaviors in collective consumption and the onset of chaotic regimes. We further propose an extension of the model in which we investigate the interdependence between the evolution of collective consumption choices and the evolution of the structure of the groups in a framework in which individuals may change the structure of preferences and then switch between being of one type or another. In the extension, we analyze how both consumption cycles (and then fashion cycles) and the evolution of the groups may lead to the emergence of chaotic dynamics, as well as the coexistence of attractors.