Emergence of Self-Organization in Animal and Human Societies

Emergence of self-organization in animal and human societies Complex systems are entities consisting of interacting agents without leaders where spatio-temporal structures can spontaneously emerge from the local interactions between these agents. They exhibit remarkable self-organization abilities which are yet poorly understood. Biology and social sciences provide many examples of complex systems (e.g. fish schools, insect swarms, bird flocks, car traffic networks, crowds, internet, supply chains, social networks, etc.). Understanding how self-organization emerges from local interactions presents a vast challenge and requires a synergetic effort between many different disciplines. It has wide variety of potential applications, such as the design and control of intelligent systems. Complex systems are usually modeled through ‘Individual-Based’ or ‘Agent-based’ models (in short, IBM’s or ABM’s). IBM’s or ABM’s try to reproduce the behavior of all interacting agents individually. Other kinds of models, ‘continuum models’, aim at describing the system through statistical averages, like in a fluid (e.g. by describing a crowd through a density of individuals instead of following the motion of each individual). Each kind of models has its own merits and drawbacks In a first part of this talk, we will show how modeling complex systems as a continuum can provide useful insights into the morphogenetic properties of the system. As an example, we will study how structures may form by simple geometric non-overlapping constraints. Examples of such occurrences are traffic jams, which are mostly related to the ‘finite size’ of the vehicles. The non-overlapping constraint is also central to the dynamics of human crowds or herds of gregarious animals. In a second part of this talk, we will discuss the relation between the two kinds of models. Classical statistical mechanics provides a correspondence between a given IBM and its associated continuum model. But its methodologies are challenged by complex systems and one of its corner-stones, the concept of ‘propagation of chaos’ breaks down for very simple ‘self-organizing’ IBM’s. We will discuss the consequences of this key observation for the future developments of this theory.