Modeling Multi-Agent Self-Organization through the Lens of Higher Order Attractor Dynamics

Abstract

Social interaction occurs across many time scales and varying numbers of agents; from one-on-one to large-scale coordination in organizations, crowds, cities, and colonies. These contexts, are characterized by emergent self-organization that implies higher order coordinated patterns occurring over time that are not due to the actions of any particular agents, but rather due to the collective ordering that occurs from the interactions of the agents. Extant research to understand these social coordination dynamics (SCD) has primarily examined dyadic contexts performing rhythmic tasks. To advance this area of study, we elaborate on attractor dynamics, our ability to depict them visually, and quantitatively model them. Primarily, we combine difference/differential equation modeling with mixture modeling as a way to infer the underlying topological features of the data, which can be described in terms of attractor dynamic patterns. The advantage of this approach is that we are able to quantify the self-organized dynamics that agents exhibit, link these dynamics back to activity from individual agents, and relate it to other variables central to understanding the coordinative functionality of a system's behavior. We present four examples that differ in the number of variables used to depict the attractor dynamics (1, 2, and 6) and range from simulated to non-simulated data sources. We demonstrate that this is a flexible method that advances scientific study of SCD in a variety of multi-agent systems.

Keywords: agent-based modeling; attractors; dynamical systems; multi-agent coordination; social coordination dynamics.

Figures

Figure 1

Time series of the headings for 300 flocking agents. Note that the flock moves toward a very restricted heading.

Figure 2

Time series of the average posterior probabilities for each attractor dynamic pattern. All patterns were attractors as indicated by their negative slopes, but differed in terms of their set points (SP; the heading in which the agents were attracted toward) and the attractor strengths (the steepness of their slopes). At around iteration 300, the system shows a phase transition wherein two patterns with the same heading begin to dominate.

Figure 3

Screenshot of nest and food placement of the Ants model from Netlogo.

Figure 4

Kernel density plot of where the ants spent most of their time during the simulation. Note that the highest densities correspond to the three food source locations and the nest.

Figure 5

(A-C) Three example ant trails that illustrate how the ant behavior is shared across all the ants while each ant had unique behavior.

Figure 6

Topographical illustration of the seven equation solution for the Ant simulation.

Figure 7

Time series plot of the amount of food available in each of the three food piles. The legend describes where in the coordinate space a given food pile was located (see also Figure 3).

Figure 8

Topographical solution for the Baboon gps data.

Figure 9

Average posterior probabilities associated with each equation group, by baboon. F is for female and M is for male.

Figure 10

(A,B) Two network diagrams that illustrate the two different equations. Beginning of arrows represent value at time t. Arrow heads represent change in value.