Formulation of Impulsive Ecological Systems Using the Conformable Calculus Approach: Qualitative Analysis

Anatoliy Martynyuk, Gani Stamov, Ivanka Stamova () and Ekaterina Gospodinova
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Anatoliy Martynyuk: S.P. Timoshenko Institute of Mechanics, NAS of Ukraine, 03057 Kiev-57, Ukraine
Gani Stamov: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Ivanka Stamova: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Ekaterina Gospodinova: Department of Computer Sciences, Technical University of Sofia, 8800 Sliven, Bulgaria

Mathematics, 2023, vol. 11, issue 10, 1-15

Abstract: In this paper, an impulsive conformable fractional Lotka–Volterra model with dispersion is introduced. Since the concept of conformable derivatives avoids some limitations of the classical fractional-order derivatives, it is more suitable for applied problems. The impulsive control approach which is common for population dynamics’ models is applied and fixed moments impulsive perturbations are considered. The combined concept of practical stability with respect to manifolds is adapted to the introduced model. Sufficient conditions for boundedness and generalized practical stability of the solutions are obtained by using an analogue of the Lyapunov function method. The uncertain case is also studied. Examples are given to demonstrate the effectiveness of the established results.

Keywords: Lotka–Volterra system; conformable derivative; impulses; practical stability; manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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