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Y. N. Xiao, D. Z. Cheng and H. S. Qin, “Optimal Impul sive Control in Periodic Ecosystem,” Systems & Control Letters, Vol. 55, No. 7, 2006, pp. 558-565. http://dx.doi.org/10.1016/j.sysconle.2005.12.003

has been cited by the following article:

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

  AUTHORS: Oleksandr Karelin, Anna Tarasenko, Manuel Gonzalez-Hernandez

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

  JOURNAL NAME: Applied Mathematics, Vol.4 No.10, September 29, 2013

  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.