Chaotic dynamical systems: an introduction

In his Memoirs, Stigler (1988, p. 78) observed that economic "theorists like new and strange constructs that create a new world or change the way of looking at the current one". I f this is a correct description of the preferences of economic theorists, one ought to expect continued interest in the fascinating development of the literature on dynamical systems and complexity. The literature certainly offers a variety of 'new and strange constructs ' , and forces us to look at some of the old issues f rom a different perspective. The advances over the last two decades have been due to truly multi-disciplinary efforts, and have benefited f rom a collaboration between the more 'abstract ' analytical work and a careful exploration of 'concrete ' examples through increasingly sophisticated computer experiments. The first "break through" for dynamic economic theory and stability analysis "probably occurred during the twenties and thirties thanks to economists such as Frisch, Tinbergen, Kalecki, Robertson, Lundberg and Hicks;" and Samuelson's Foundations also played its role " to set the stage for further theoretical work" [Lindbeck (1970)]. A useful compendium of the trade cycle models of Hicks, Samuelson, Goodwin, Kalecki and Phillips was available in Allen (1956), and a number of the classic papers were compiled in Cass and McKenzie (1974). Subsequent research in dynamic economics continued in several directions, involving descriptive models of growth and market disequilibrium as well as models involving intertemporal optimization with their duals interpreted as intertemporal equilibria. By now we have a relative abundance of examples which generate complex