×

Self-regulation in infinite populations with fission-death dynamics. (English) Zbl 1404.92155

Summary: The evolution of an infinite population of interacting point entities placed in \(\mathbb{R}^d\) is studied. The elementary evolutionary acts are death of an entity with rate that includes a competition term and independent fission into two entities. The population states are probability measures on the corresponding configuration space and the result is the construction of the evolution of states in the class of sub-Poissonian measures, that corresponds to the lack of clusters in such states. This is considered as a self-regulation in the population due to competition.

MSC:

92D25 Population dynamics (general)
92D15 Problems related to evolution
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Hamsa, K.; Jagers, P.; Klebaner, F. C., On the establishment, persistence, and inevitable extinction of populations, J. Math. Biol., 797-820, (2016) · Zbl 1334.60179
[2] Klebaner, F. C.; Sagitov, S.; Vatutin, V. A.; Haccou, P.; Jagers, P., Stochasticity in the adaptive dynamics of evolution: the bare bones, J. Biol. Dyn., 5, 147-162, (2011) · Zbl 1403.92180
[3] Kondratiev, Yu.; Kozitsky, Yu., Self-regulation in the bolker-pacala model, Appl. Math. Lett., 69, 106-112, (2017) · Zbl 1381.92082
[4] Kozitsky, Yu.; Tanaś, A., Evolution of states of an infinite fission-death system, (2018)
[5] Ruelle, D., Superstable interactions in classical statistical mechanics, Commun. Math. Phys., 18, 127-159, (1970) · Zbl 0198.31101
[6] Simon, B., The statistical mechanics of lattice gases. vol. I, Princeton Series in Physics, (1993), Princeton University Press Princeton, NJ · Zbl 0804.60093
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.