This paper is concerned with the mathematical analysis of a deterministic model describing animal orientation as it appears, e.g., in fish schools of relatively large size.
The governing quasilinear differential equation is of diffusion type including integral terms that describe distribution phenomena.
Firstly, the authors prove local existence, uniqueness, and positivity of mild solutions via semigroup techniques in an \(L^2\)-setting. Global existence is then established for positive solutions. Moreover, a regularity result is provided showing that a mild solution is a classical one if the initial data are smooth enough.
Secondly, the existence of a stable steady state is shown, the asymptotic behaviour is analysed, and bifurcation is studied in detail. So it turns out, e.g., that below a certain threshold dispersion dominates over gregarism (adoption of the dominant orientation).
Finally, some computational aspects regarding the bifurcation branch are discussed.