Emergence in stigmergic and complex adaptive systems: A formal discrete event systems perspective

Complex systems have been studied by researchers from every discipline: biology, chemistry, physics, sociology, mathematics and economics and more. Depending upon the discipline, complex systems theory has accrued many flavors. We are after a formal representation, a model that can predict the outcome of a complex adaptive system (CAS). In this article, we look at the nature of complexity, then provide a perspective based on discrete event systems (DEVS) theory. We pin down many of the shared features between CAS and artificial systems. We begin with an overview of network science showing how adaptive behavior in these scale-free networks can lead to emergence through stigmergy in CAS. We also address how both self-organization and emergence interplay in a CAS. We then build a case for the view that stigmergic systems are a special case of CAS. We then discuss DEVS levels of systems specifications and present the dynamic structure extensions of DEVS formalism that lends itself to a study of CAS and in turn, stigmergy. Finally, we address the shortcomings and the limitation of current DEVS extensions and propose the required augmentation to model stigmergy and CAS.