摘要
A new approach to modeling populations incorporating stochasticity,a random environment,and individual behavior is illustrated with a specific example of two interacting populations:rabbits and grass.The derivation of the system of stochastic partial differential equations(SPDEs)to show how the individual mechanisms of both populations are included.This model also has an unusual feature of a nonlocal term.The harvesting of the rabbit population is introduced as a control variable.
基金
the input from the Optimal Control of Agent-based Model Working Group at the National Institute for Mathematical and Biological Synthesis,which is sponsored by the National Science Foundation through NSF Award DBI-1300426
support from the University of Tennessee,Knoxville
partially supported by the Department of Mathematics of the University of Tennessee
partially supported by Southern University of Science and Technology Start up fund Y01286120
National Science Fundation of China grants 61873325 and 11831010
partially supported by NSF under grants DMS-1007514 and DMS-1406776。
