A predator–prey interaction from micro to macro perspectives - Wang, Huaying; Pang, Yulei; Zhang, Luona; Martin, Clyde F (Nonlinear Dynamics, 2015)
This paper deals with predator–prey dynamics in individual and population perspectives. First, we build a discrete Markov model on predator–prey interactions in individual perspective. By shortening the time gap, from discrete time to continuous time, and increasing the number of individuals to infinity, a continuity equation on the predator–prey interactions is derived in a large population regime. Then, with the leading items of the continuity equation, that is the mean-field equation, following the approximate model, which entails qualitative analysis, we can obtain an asymptotically stable closed orbit or simply put, the parameter conditions where equilibrium point exists. These qualitative conclusions are the performance of individual microscopic interactions on macro-level groups, or can be treated as one component of microscopic models of various random statistical average results.This paper explored the accuracy and operability of the model constructed on individual level, which differs from traditional method, constructing population model directly via differential equations and difference equations. Therefore, by operating variables and data from individual behavior, it is probable for us to construct more accurate models for population dynamic. © 2014, Springer Science+Business Media Dordrecht (outside the USA).
1 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/041-431-988-565-054 tex.type: [object Object]
Keywords: Asymptotically stable; Continuity equation; Continuity equations; Continuous time systems; Difference equations; Differential equations; Discrete Markov model; Individual interaction; Macro-level groups; Markov processes; Microscopic interaction; Parameter conditions; Population statistics; Predator prey systems; Qualitative analysis; Stable limit cycle; dept.mat