Emergence in stigmergic and complex adaptive systems: A formal discrete event systems perspective
Introduction
A natural system is not a monolithic system but a heterogeneous system made up of disparity and dissimilarity, devoid of any larger goal. The system just “is.” Examples of such systems include ant colonies, the biosphere, the brain, the immune system, the biological cell, businesses, communities, social systems, stock markets, etc. Such systems are adaptable systems where emergence and self-organization are factors that aid evolution. These systems are classified as complex adaptive systems. According to Holland (2006, p. 1): “CAS are systems that have a large number of components, often called agents that interact and adapt or learn.”
In this article, we investigate CAS by looking at the scale of components, interactions between the components, and emergent properties that are manifested by such CAS. We will attempt to understand some of the common underlying properties, address the adaptive nature of such complex systems and illustrate how resilience is an inherent property of CAS.
CAS is occasionally modeled by means of agent-based models and complex network-based models. Multi-agent systems (MASs) is the area of research that deals with such study. However, CAS is fundamentally different from MAS in portraying features like self-similarity (scale-free), complexity, emergence and self-organization that are at a level above the interacting agents. A CAS is a complex, scale-free collectivity of interacting adaptive agents, characterized by high degree of adaptive capacity, giving them resilience in the face of perturbation. Indeed, designing an artificial CAS requires formal attention to these specific features. We will address these features and the formalisms needed to model CAS.
The discipline of modeling originated to understand natural phenomena. By developing abstractions, we can manage the apparent complexity, reuse it and enable these complex phenomena in artificial systems to our advantage. The discipline of executing this model on a time base is “simulation.” The task of decoding the original structure from manifested behavior is the holy grail of the modeling and simulation (M & S) enterprise (Zeigler, Praehofer, & Kim, 2000). The need for M & S to make progress in understanding CAS has been well acknowledged by Holland (1992). The task is to understand the gamut of rules that exist within and without a component and understand how the component deals with such multidimensional rules in an interactive environment. M & S is the only way one can understand, mimic and recreate a natural system. Most artificially modeled systems that exhibit complex adaptive behavior are driven by multi-resolution bindings and interconnectivity at every level of system behavior. To understand life is to “model”; to adapt is to survive in an environment, where both survival and environment are loaded concepts based on the guiding discipline.
Complexity is a phenomenon that is multivariable and multi-dimensional in a space–time continuum. Therefore, what we need is a framework that helps develop system structure and behavior in an abstract manner and that is component oriented so that the system can define its interactions based on the composition of a multi-level environment.
Stigmergy, the study of indirect interaction between network components in a persistent environment, explains certain emergent properties of a system. The network components include both the environment and the agent and both are persistent, i.e. both are situated in a space–time continuum and have memory. We take stigmergic systems to be a subset of CAS and argue that stigmergic behavior is an emergent phenomenon too. Ultimately, we are trying to get a handle on how to formalize the property of “emergence.”
Discrete event abstraction has been studied at length by Bernard Zeigler throughout his illustrious career and his pioneering work on discrete event systems (DEVS) formalism in 1970s (Zeigler, 1976). As a student, his perspectives on CAS were influenced by Holland. Ziegler’s approach to CAS has been through the quantization of continuous phenomena and how quantization leads to abstraction. Any CAS must operate within the constraints imposed by space, time, and resources on its information processing (Pinker, 1997). Evidence from neuronal models and neuron processing architectures and from fast and frugal heuristics, provide further support to the centrality of discrete event abstraction in modeling CAS when the constraints of space, time and energy are taken into account. Zeigler stated that discrete event models are the right abstraction for capturing CAS structure and behavior (Zeigler, 2004). In this article, we take the discipline of modeling CAS forward, by looking at the emergence aspect of CAS. We introduce DEVS and demonstrate how recent extensions still fall a little short in modeling CAS.
We first focus on the study of network science and how scale-free networks are inherently important to study complex interactions and hierarchical systems. In Section 3 we look at various types of interactions in a complex network. Section 4 we address the concepts of emergence and self-organization in detail and examine how a complex dynamic network facilitates such behavior. Section 5, a slight digression, provides an overview of DEVS theory. We return to the subject of dynamism in a complex adaptive network in Section 6 and show how DEVS theory is positioned to give modeling and simulation support to the subject. We describe various existing formal DEVS extensions that help model various features of stigmergy, emergence and CAS. Finally, in Section 7, we present some conclusions and pointers for future research.
Section snippets
Overview
Complex networks are the backbone of complex systems and each complex system is a network of interactions among numerous network elements. Some networks are geometric or regular in 2D or 3D space and some have “long range” connections that are not spatial at all. Network topology or anatomy is important to characterize because structure affects function and vice versa. The dynamic nature of a network is one of the keys to understand complexity. Each network comes with peculiar set of properties
The nature of actions in a complex adaptive system
In this section we take a look at different types of actions that impact the evolution of the network. We classify these actions into two broad categories, i.e., intra-actions and inter-actions.
Intra-actions: These are the actions taken by the node internally, i.e., these actions impact the node itself first and may impact other nodes through various interactions this node participates in. These actions are initiated by the internal dynamics of the node.
Inter-actions: These are the actions
Emergence and self-organization
Emergence, a term coined by Lewes (1875) has gained widespread attention in the last two decades partly due to the analysis capabilities afforded by massive computational power and partly due to widespread complex systems in everyday use such as World Wide Web. Emergence has been a native of the land of “complex systems” and there are four schools of thought that study emergence, as summarized by Wolf and Holvoet (2005):
- 1.
Complex adaptive systems theory: Concept of macro-level patterns arising
Discrete event systems (DEVS) theory and its variants
The Theory of Modeling and Simulation was first introduced in (Zeigler, 1976). Some notable extensions of the original DEVS formalism are fuzzy DEVS, dynamic structure DEVS, confluent DEVS, symbolic DEVS and real-time DEVS. DEVS concepts have been applied to almost every natural phenomenon, from simple state machines to non-linear systems to continuous systems to complex hybrid systems (Zeigler et al., 2000). The depth of DEVS systems formalism was acknowledged by researchers like (Vangheluwe,
DEVS for complex adaptive systems
The feature list presented in Table 4 list just some of the features that we identified and that can help in modeling CAS with DEVS. Our analysis is based on scale-free topologies and co-occurrence of self-organization and emergence in an interconnected network of persistent agents and persistent environments. We also established that a stigmergic system is a type of CAS so the features categorized as “SG” in Table 4 are also applicable to CAS. The last column shows the state-of-the-art in
Conclusions
Complexity is a multifaceted topic and each complex system has its own properties. However, some of the properties like high interconnectedness, large number of components, and adaptive behavior are present in most natural complex systems. We looked at the mechanism behind interconnectedness using network science that describes many natural systems in the light of power laws and self-similar scale-free topologies. Such scale-free topologies bring their own inherent properties to the complex
Acknowledgements
We would like to thank Margery J. Doyle for her expert knowledge on agent-based stigmergic behavior. We also thank reviewers for making insightful comments thereby increasing the quality of the article. Lastly, we thank our editors Leslie Marsh and Margery J. Doyle for their help in preparation of the manuscript.
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