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Stationary distributions in Kolmogorov-Petrovski- Piskunov-type models with an infinite number of particles

Published on Jul 3, 2017in Mathematical Population Studies0.276
· DOI :10.1080/08898480.2017.1330010
Stanislav Molchanov28
Estimated H-index: 28
(HSE: National Research University – Higher School of Economics),
Joseph M. Whitmeyer13
Estimated H-index: 13
(UNCC: University of North Carolina at Charlotte)
Abstract
A model of population dynamics in continuous time on the lattice contains the Kolmogorov-Petrovski-Piskunov equation as a special case. A limit distribution exists. The first three moments and the correlation function are expressed.
  • References (9)
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References9
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A continuous-time branching random walk on multidimensional lattices with a finite number of branching sources of three types leads to explicit conditions for the exponential growth of the total number of particles. These conditions are expressed in terms of the spectral characteristics of the operator describing the mean number of particles both at an arbitrary point and on the entire lattice.
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#1Elena Yarovaya (MSU: Moscow State University)H-Index: 9
We introduce a model of continuous-time branching random walk on a finite-dimensional integer lattice with finitely many branching sources of three types and study the spectral properties of the operator describing the evolution of the mean numbers of particles both at an arbitrary source and on the entire lattice. For the leading positive eigenvalue of the operator, we obtain existence conditions determining exponential growth in the number of particles in this model.
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For the critical branching random walk on the lattice ${{\mathbb Z}^d}Zd, in the case of an arbitrary total number of produced offspring spreading on the lattice from the parental particle, the existence of a limit distribution (which corresponds to a steady state (or statistical equilibrium)) of the population is proved. If the second factorial moment of the total number of offspring is much larger than the square of the first factorial moment, then the limit particle field displays strong d...
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