20214 5 108498 2 328517 document 108498 mathematics-12-04033.pdf application/pdf 09959cd6054ad86fa97ff60d04608956 MD5 608069 2025-01-07 09:00:01 https://pure.iiasa.ac.at/id/eprint/20214/1/mathematics-12-04033.pdf 20214 1 1 application/pdf text en public cc_by_4

mathematics-12-04033.pdf

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/108498 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/108498 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/108498 archive 353 disk0/00/02/02/14 2025-01-07 09:01:52 2025-01-07 09:01:52 2025-01-07 09:01:52 article show Nikolaev M. Nikitin A. Dieckmann U. 1668 0000-0001-7089-0393 pub ASA CAT EM SYRR nonlinear integral equations; spatial logistic dynamics; individual-based models; fixed-point We investigate a nonlinear integral equation derived through moment approximation from the individual-based representation of spatial logistic dynamics. The equation describes how the densities of pairs of individuals represented by points in continuous space are expected to equilibrate under spatially explicit birth–death processes characterized by constant fecundity with local natal dispersal and variable mortality determined by local competition. The equation is derived from a moment hierarchy truncated by a moment closure expressing the densities of triplets as a function of the densities of pairs. Focusing on results for individuals inhabiting two-dimensional habitats, we explore the solvability of the equation by introducing a dedicated space of functions that are integrable up to a constant. Using this function space, we establish sufficient conditions for the existence of solutions of the equation within a zero-centered ball. For illustration and further insights, we complement our analytical findings with numerical results. 2024-12-23 published MDPI doi:10.3390/math12244033 66 public Mathematics 12 24 e4033 TRUE 2227-7390 info:eu-repo/semantics/article