### On the closure of spatial moments in the biological model, and the integral equations to which it leads

#### Abstract

#### Full Text:

PDF (Russian)#### References

Warshel A. Multiscale modeling of biological functions: from enzymes to molecular machines (Nobel Lecture). // Angew Chem. Int. Ed. Engl. – 2014. – Sept – Vol. 53, no. 38.

Alekseev V.R., Kazanceva T.I. Ispol'zovanie individual'no-orientirovannoj modeli dlja izuchenija roli materinskogo jeffekta v smene tipov razmnozhenija u Cladocera // Zhurnal obshhej biologii. –

– t.68, #3. – 231-240. (in russian)

Alexeev V., Lampert W. Maternal control of resting-egg production in Daphnia // Nature. – 2001. – Vol. 414 – 899-901.

Dieckmann U., Law R. Introduction // The Geometry of Ecological Interactions: Simplifying Spatial Complexity / ed. by U. Dieckmann, R. Law, J. Metz. – Cambridge University Press, 2000. – 1-6.

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. – 252-270.

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. – 412-455.

Bodrov A. G., Nikitin A. A. Qualitative and numerical analysis of an integral equation arising in a model of stationary communities // Doklady Mathematics. — 2014. — Vol. 89, no. 2. — P. 210–213.

Bodrov A. G., Nikitin A. A. Examining the biological species steady-state density equation in spaces with different dimensions // Moscow University Computational Mathematics and Cybernetics. — 2015. — Vol. 39, no. 4. — P. 157–162.

Kalistratova A. V., Nikitin A. A. Study of dieckmann’s equation with integral kernels having variable kurtosis coefficient // Doklady Mathematics. — 2016. — Vol. 94, no. 2. — P. 574–577.

Nikitin A. A., Savostianov A. S. Nontrivial stationary points of two-species self-structuring communities // Moscow University Computational Mathematics and Cybernetics. — 2017. — Vol. 41, no. 3. — P. 122– 129.

Nikitin A.A., Nikolaev M.V. Equilibrium Integral Equations with Kurtosian Kernels in Spaces of Various Dimensions // Moscow University Computational Mathematics and Cybernetics. — 2018. — Vol. 42, no. 3. — P. 105–113.

Bolker B., Pacala S. Using moment equations to understand stochastically driven spatial pattern formation in ecological systems // Theoretical Population Biology. – 1997. – Vol. 52.

Murrel D.J., Dieckmann U., Law R. On moment closures for population dynamics in continuous space // Journal of Theoretical Biology. – 2004. – Vol. 229. – 421-432

Danchenko V.I., Davydov A.A., Nikitin A.A. Ob integral'nom uravnenii dlja stacionarnyh raspredelenij biologicheskih soobshhestv // Problemy dinamicheskogo upravlenija. – 2010. - #3. – 15-29. (in russian)

A.A. Davydov, V.I. Danchenko, M.Yu. Zvyagin, 2009, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 267, pp. 46–55.

Danchenko V.I., Rubaj R.V. Ob odnom integral'nom uravnenii stacionarnogo raspredelenija biologicheskih sistem. // Sovremennaja matematika. Fundamental'nye napravlenija. Tom 36 (2010). 50-60. (in russian)

Seier E., Bonett D. Two families of kurtosis measures // Metrika. 2003. 58. 59-70.

Verhulst P.F. Notice sur la loi que la population poursuit dans son accroissement // Correspondance mathematique et physique. – 1838. – Vol. 10. – 113- 121.

### Refbacks

- There are currently no refbacks.

Abava FRUCT 2019

ISSN: 2307-8162