diff --git a/article/content.tex b/article/content.tex index be62a8e..866cedb 100644 --- a/article/content.tex +++ b/article/content.tex @@ -36,7 +36,7 @@ \section{Introduction} \section{Methods} The model formulation used in this paper is the same as in the original -publication. \citeauthor{hastings1991} used a 14 parameter model to represent the three-species +publication. \citeauthor{hastings1991} used a continuous-time model with 14 parameters to represent the three-species food chain, with $X$, $Y$, and $Z$ as the numbers of the species at the lowest level of the food chain, of the species that preys upon $X$, and of the species that preys upon $Y$, respectively. @@ -145,11 +145,11 @@ \section{Methods} dynamics. Moreover, \citeauthor{hastings1991} mention removing points resulting from secondary local maxima, but do not provide details on how to identify these points. Hence, we adopted the following method: -1) we let the system run for time steps between 0 and 10 000, then kept the 1000 last -solutions to the numerical integration for $z$ to eliminate transient behaviour +1) we let the system run for continuous time steps between 0 and 10 000, then kept the last 1000 +solutions to the numerical integration to eliminate transient behaviour (note that these do not occur at time steps between 9000 and 10 000, as the system doesn't necessarily reach a stable solution, and that the exact time steps vary for all values of $b_1$); -2) we selected the values that were greater than both their preceding and following +2) we selected the values of $z$ that were greater than both their preceding and following values, which identified local maxima only; and 3) we only kept values that were greater than a given threshold of the cycle's maximal amplitude, in order to remove secondary local maxima.