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In an article in the journal Science, Norbert Juergens, a professor of ecology at the University of Hamburg, said these termites "match the beaver with regard to intensity of environmental change, but surpass it with regard to the spatial dimension of their impact".
When (R_{0}le1) we prove the disease-free equilibrium is stochastically asymptotically stable in the large, which is independent of the intensity of environmental white noise.
Consequently, (lambda,dt tolambda,dt +sigma,dB_{t}), where (B_{t}) is a standard Brownian motion, (sigma^{2}>0) is the intensity of environmental white noise.
Our analysis results and numerical simulations reveal that the intensity of environmental fluctuation plays a crucial role for the survival of susceptible, infected prey and predator species.
To a great extent, when the intensity of environmental noise is not too big, some nice properties such as non-explosion, boundedness, permanence are desired.
From the above numerical simulations and discussions, we can conclude that both heavy intensity of environmental noises and large impulsive perturbations to the ecological system will lead to the extinction of the species.
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where σ 1 2 and σ 2 2 are known as the intensities of environmental noise.
And since our purpose is to reveal the effect of environmental noises, we impose the following hypothesis on intensities of environmental noises.
It tells us that when the intensities of environmental noises are not too big, some nice properties such as non-explosion, boundedness, and permanence are desired.
Here, it suggests that even if during the life course the intensity of the environmental stresses remained constant, the average recovery time would still increase with age.
Here, we apply a stochastic dynamics framework to illustrate that the average number of deficits present in an individual is the product of the average intensity of the environmental stresses and the average recovery time.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com