Vector Fixed Point Approach to Control of Kolmogorov Differential Systems

Authors

  • Alexandru Hofman Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
  • Radu Precup Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

DOI:

https://doi.org/10.37256/cm.5220242840

Keywords:

Kolmogorov system, control problem, fixed point, matrix convergent to zero, differential equations and systems, Volterra-Fredholm integral equation, Lotka-Volterra system

Abstract

The paper presents a vector approach to control problems for systems of equations. The method is described in the case of Kolmogorov systems which arise frequently in the dynamics of populations. Three types of problems are discussed: problems with control of both per capita growth rates, problems with control parameters acting on the growth rates, and problems which combine the first two types. The controllability is obtained via a vector approach based on the Perov fixed point theorem and matrices which are convergent to zero. Four concrete illustrative examples are added.

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Published

2024-04-29

How to Cite

1.
Hofman A, Precup R. Vector Fixed Point Approach to Control of Kolmogorov Differential Systems. Contemp. Math. [Internet]. 2024 Apr. 29 [cited 2024 May 27];5(2):1968-81. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2840