- PII
- 10.31857/S2686954324010074-1
- DOI
- 10.31857/S2686954324010074
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 515 / Issue number 1
- Pages
- 44-49
- Abstract
- The work is devoted to the analysis of a nonlinear integral equation that arises as a result of parametric closure of the third spatial moment in a single-species model of logistic dynamics by U. Dieckmann and R. Law. The case of piecewise constant kernels is analyzed, which is very important for further computer modeling. Sufficient conditions have been found to guarantee the existence of a nontrivial solution to the equilibrium equation. The use of constant kernels made it possible to obtain more accurate results compared to earlier works, in particular, more accurate estimates were obtained for the norm of the solution, as well as for the closure parameter.
- Keywords
- функциональный анализ нелинейные интегральные уравнения математическая биология
- Date of publication
- 15.11.2024
- Year of publication
- 2024
- Number of purchasers
- 0
- Views
- 44
References
- 1. Law R., Dieckmann U. Moment approximations of individual-based models // The Geometry of Ecological Interactions: Simplifying Spatial Complexity / Ed. by U. Dieckmann, R. Law, J. Metz. Cambridge University Press, 2000. P. 252–270.
- 2. Dieckmann U., Law R. Relaxation projections and the method of moments // The Geometry of Ecological Interactions: Simplifying Spatial Complexity / Ed. by U. Dieckmann, R. Law, J. Metz. Cambridge University Press. 2000. P. 412–455.
- 3. Murrell D.J., Dieckmann U., Law R. On moment closures for population dynamics in continuous space // J. Theor. Biology. 2004. Vol. 229. P. 421–432.
- 4. Красносельский М.А. Два замечания о методе последовательных приближений // УМН. 1955. 10:1(63). С. 123–127.
- 5. Никитин А.А., Николаев М.В. Принцип Лере–Шаудера в применении к исследованию одного нелинейного интегрального уравнения // Дифференциальные уравнения. 2019. Т. 55. С. 1209–1217.
