Application of Functional Operators with Shift to the Study of Renewable Systems When the Reproductive Process Is Described by Integrals with Degenerate Kernels

Affiliation(s)

Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico.

Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico.

Abstract

We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.

Keywords

Renewable Resource; Equilibrium State; Holder Space; Reproductive Process; Inverse Operator

Renewable Resource; Equilibrium State; Holder Space; Reproductive Process; Inverse Operator

Cite this paper

Karelin, O. , Tarasenko, A. and Gonzalez-Hernandez, M. (2013) Application of Functional Operators with Shift to the Study of Renewable Systems When the Reproductive Process Is Described by Integrals with Degenerate Kernels.*Applied Mathematics*, **4**, 1376-1380. doi: 10.4236/am.2013.410186.

Karelin, O. , Tarasenko, A. and Gonzalez-Hernandez, M. (2013) Application of Functional Operators with Shift to the Study of Renewable Systems When the Reproductive Process Is Described by Integrals with Degenerate Kernels.

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