I'm more of a mathematician than a biologist, so I had a question about an application of the population growth equation to real-life models, and thus would like to ask biologists for their insights. The equation I'm looking at is the following (in reality, I have n-species but it's just an extension of this two dimensional problem):
$$ \frac{dx_1}{dt} =x_1\Big(b_1-a_{11}x_1-a_{12}x_2 \Big) $$ $$ \frac{dx_2}{dt} =x_2\Big(b_2-a_{21}x_1-a_{22}x_2 \Big) $$
where the $b$ are growth parameters, and the $a$'s are all parameters describing interactions among the species (and carrying capacity). The papers I've looked at for stochastic perturbations with these equations have primarily dealt with stochastically perturbing either the $b$ parameters while holding the others constant, or perturbing the $a$ parameters while holding $b$'s constant. However, these papers are written by mathematicians with no biological experience, so the decision on which sets of parameters to perturb are somewhat arbitrarily decided without any biological basis.
For the biologists, can someone suggest some cases for where it would be more biologically reasonable to perturb the growth parameters and some cases were it would make more biological sense to perturb the interacting parameters? I ask because I'm a part of some interdisciplinary neuroscience project which is using equations of this form to study interacting neuron clusters, but since I'm a math person and not a biologist, I am trying to understand reasonable explanations for what stochastic perturbations mean biologically for these parameters.
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