Modeling group formation and activity patterns in self-organizing collectives of individuals. (English) Zbl 1298.92121
Summary: We construct and analyze a nonlocal continuum model for group formation with application to self-organizing collectives of animals in homogeneous environments. The model consists of a hyperbolic system of conservation laws, describing individual movement as a correlated random walk. The turning rates depend on three types of social forces: attraction toward other organisms, repulsion from them, and a tendency to align with neighbors. Linear analysis is used to study the role of the social interaction forces and their ranges in group formation. We demonstrate that the model can generate a wide range of patterns, including stationary pulses, traveling pulses, traveling trains, and a new type of solution that we call zigzag pulses. Moreover, numerical simulations suggest that all three social forces are required to account for the complex patterns observed in biological systems. We then use the model to study the transitions between daily animal activities that can be described by these different patterns.
MSC:
| 92D50 | Animal behavior |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35L60 | First-order nonlinear hyperbolic equations |
| 35L65 | Hyperbolic conservation laws |
| 91D30 | Social networks; opinion dynamics |
Keywords:
nonlocal hyperbolic system; group formation; social interactions; spatial patterns; zigzag movementSoftware:
BoidsReferences:
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