Flashing annihilation term of a logistic kinetic as a mechanism leading to Pareto distributions

TL;DR

This paper demonstrates analytically that a flashing annihilation term in a logistic kinetic model results in Pareto power-law distributions at equilibrium, and introduces a quasideterministic Levy noise source for slow switching frequencies.

Contribution

It reveals how a flashing annihilation term can produce Pareto distributions and Levy noise in a logistic kinetic framework, providing new insights into complex stochastic processes.

Findings

Flashing annihilation leads to Pareto power-law distributions.

Slow switching frequency induces Levy noise at the macroscopic level.

Analytical proof of the distribution emergence in the model.

Abstract

It is shown analytically that the flashing annihilation term of a Verhulst kinetic leads to the power--law distribution in the stationary state. For the frequency of switching slower than twice the free growth rate this provides the quasideterministic source of a Levy noises at the macroscopic level.