Abstract
Direction-dependent interaction rules are incorporated into a one-dimensional discrete-time stochastic individual-based model (IBM) of collective behavior to compare pattern formation with an existing partial differential equation (PDE) model. The IBM is formulated in terms of three social interaction forces: repulsion, alignment, and attraction, and includes information regarding conspecifics’ direction of travel. The IBM produces a variety of spatial patterns which qualitatively match patterns observed in a PDE model. The addition of direction-dependent interaction rules exemplifies how directional information transfer within a group of individuals can result in enriched pattern formation. Our individual-based modelling framework reveals the influence that direction-dependent interaction rules such as biological communication can have upon individual movement trajectories and how these trajectories combine to form group patterns.
Highlights
Flocks of birds, schools of fish, and insect swarms are examples of collective behavior exhibited by animals
For the purposes of investigating the effect of incorporating direction-dependent interaction rules on the formation of spatial patterns, we focus on individual-based model (IBM) for three reasons
We describe the development of the IBM by imposing social interaction kernels on a stochastic individual-based model, and define 5 submodels which prescribe different direction-dependent interaction rules
Summary
Schools of fish, and insect swarms are examples of collective behavior exhibited by animals. These groups of animals form spatial patterns as individuals coordinate their movements in efforts to search for a mate, forage for sustenance, or evade predation. We do not include external factors such as environmental conditions or spatial structures that lead to group formation, but instead focus on those spatial patterns that result from interactions between conspecifics. Within this context, there are two general methodologies for studying collective behavior.
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