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Entropy
Volume 22
Issue 9
10.3390/e22090970
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Article

Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior

by
Rohisha Tuladhar
1,†,
Fidel Santamaria
1,† and
Ivanka Stamova
2,*,†
1
Department of Biology, University of Texas at San Antonio, San Antonio, TX 78249, USA
2
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Entropy 2020, 22(9), 970; https://doi.org/10.3390/e22090970
Submission received: 1 August 2020 / Revised: 26 August 2020 / Accepted: 27 August 2020 / Published: 31 August 2020
(This article belongs to the Special Issue Dynamics in Complex Neural Networks)
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Abstract

We present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect to sets. The proposed results extend the existing stability results for integer-order n−species delayed Lotka-Volterra cooperation models to the fractional-order case under impulsive control.
Keywords: biological Lotka-Volterra cooperation networks; fractional derivatives; impulsive control; Mittag-Leffler stability; practical stability; stability of sets biological Lotka-Volterra cooperation networks; fractional derivatives; impulsive control; Mittag-Leffler stability; practical stability; stability of sets

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MDPI and ACS Style

Tuladhar, R.; Santamaria, F.; Stamova, I. Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior. Entropy 2020, 22, 970. https://doi.org/10.3390/e22090970

AMA Style

Tuladhar R, Santamaria F, Stamova I. Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior. Entropy. 2020; 22(9):970. https://doi.org/10.3390/e22090970

Chicago/Turabian Style

Tuladhar, Rohisha, Fidel Santamaria, and Ivanka Stamova. 2020. "Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior" Entropy 22, no. 9: 970. https://doi.org/10.3390/e22090970

APA Style

Tuladhar, R., Santamaria, F., & Stamova, I. (2020). Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior. Entropy, 22(9), 970. https://doi.org/10.3390/e22090970

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