Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr Individual based model with competition in spatial ecology. (English) Zbl 1185.60110 SIAM J. Math. Anal. 41, No. 1, 297-317 (2009). Summary: We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population in the course of the stochastic evolution. Cited in 2 ReviewsCited in 31 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 92D40 Ecology 82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics 82C22 Interacting particle systems in time-dependent statistical mechanics Keywords:continuous systems; spatial birth-and-death processes; correlation functions; individual based models; spatial plant ecology PDFBibTeX XMLCite \textit{D. Finkelshtein} et al., SIAM J. Math. Anal. 41, No. 1, 297--317 (2009; Zbl 1185.60110) Full Text: DOI arXiv