Abstract
We study coarse-grained (group-level) alignment dynamics of individual-based animal group models for heterogeneous populations consisting of informed (on preferred directions) and uninformed individuals. The orientation of each individual is characterized by an angle, whose dynamics are nonlinearly coupled with those of all the other individuals, with an explicit dependence on the difference between the individual's orientation and the instantaneous average direction. Choosing convenient coarse-grained variables (suggested by uncertainty quantification methods) that account for rapidly developing correlations during initial transients, we perform efficient computations of coarse-grained steady states and their bifurcation analysis. We circumvent the derivation of coarse-grained governing equations, following an equation-free computational approach.
Original language | English (US) |
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Pages (from-to) | 100-112 |
Number of pages | 13 |
Journal | Journal of Theoretical Biology |
Volume | 246 |
Issue number | 1 |
DOIs | |
State | Published - May 7 2007 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modeling and Simulation
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics
Keywords
- Coarse-graining
- Equation-free multiscale approach
- Group-level dynamics
- Heterogeneous animal group alignment
- Wiener polynomial chaos