Noise in an insect outbreak model

TL;DR

This paper investigates how Gaussian white noise affects the steady state behavior of an insect outbreak model, revealing that noise can both reduce and prevent insect extinction through phase transitions.

Contribution

It provides a detailed analysis of the steady state probability distribution and shows how different noise sources influence insect population dynamics and extinction risk.

Findings

Fluctuations in birth rate decrease insect populations.

Fluctuations in predation rate can prevent extinction.

Noise can induce phase transitions in the model.

Abstract

We study the steady state properties of an insect (spruce budworm) outbreak model in the presence of Gaussian white noise. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution function and its extrema have been investigated. It was found that fluctuations of the insect birth rate reduces the population of the insects while fluctuations of predation rate and the noise correlation can prevent the population of the insects from going into extinction. Noise in the model can induce a phase transition.