Coagulation-fragmentation model for animal group-size statistics

Abstract

We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no $H$-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on recent developments in complex function theory for Bernstein and Pick functions. In the large-population continuum limit, a scaling-invariant regime is reached in which all equilibria are determined by a single scaling profile. This universal profile exhibits power-law behavior crossing over from exponent $-\frac{2}{3}$ for small size to $-\frac{3}{2}$ for large size, with an exponential cut-off.

51 pages, 2 figures

References in corpus (4)

• Power-law versus exponential distributions of animal group sizes
• Space-irrelevant scaling law for fish school sizes
• Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance
• Numerical approximation of a coagulation-Fragmentation Model for Animal Group Size Statistics

Cited by in corpus (15)

• On the Random Batch Method for second order interacting particle systems
• On the energy cascade of 3-wave kinetic equations: Beyond Kolmogorov-Zakharov solutions
• Temporal oscillations in Becker-Doering equations with atomization
• A generalized definition of Caputo derivatives and its application to fractional ODEs
• Random batch methods (RBM) for interacting particle systems
• Localization in stationary non-equilibrium solutions for multicomponent coagulation systems
• Convergence of Random Batch Method for interacting particles with disparate species and weights
• Mean field error estimate of the random batch method for large interacting particle system
• Self-similar spreading in a merging-splitting model of animal group size
• Explicit solutions to some fragmentation equations with growth or decay
• Optimal error estimates for analytic continuation in the upper half-plane
• Long term dynamics of the discrete growth-decay-fragmentation equation
• Numerical approximation of a coagulation-Fragmentation Model for Animal Group Size Statistics
• Multicomponent coagulation systems: existence and non-existence of stationary non-equilibrium solutions
• On the mean field limit of the Random Batch Method for interacting particle systems