The Dependence Of Population Size Upon Nonlocal Dispersal Rate Of A Nonlocal Biological Model

Equations with non-local dispersal have been widely used as models in biology. In this paper, we focus on logistic models with non-local dispersal for single species. We study the number of maxima of the population size upon nonlocal dispersal rate under spatially heterogeneous environments through numerical methods. We first offer some propositions to simplify the problem. Through these propositions, we only need to study some bounded simple functions among all environment functions. Then, we construct two algorithms, the algorithm based on solving system of nonlinear equations and the algorithm based on fixed point iteration, to find the numerical solution of the problem. We also prove the convergence of the algorithm and compare our numerical results with some exist theoretical results. Finally, we do the simple random sampling of selected bounded simple functions and make the interval estimation of the proportion of at least two maxima case. Our result shows that the lower high confidence level bound of the estimated proportion is 0 while the upper bound decreases with the increase in sample.