Lotka-Volterra Model with Periodic Harvesting-Reference-Cited by-同舟云学术

Lotka-Volterra Model with Periodic Harvesting

Published:2022-12-31 Issue: Volume:21 Page:283-293
ISSN:2224-2678
Container-title:WSEAS TRANSACTIONS ON SYSTEMS
language:en
Short-container-title:

Author:

Muhtar Norma¹,Cahyono Edi¹,Iswandi R. Marsuki²,Muhidin Muhidin²

Affiliation:

1. Department of Mathematics, FMIPA, Universitas Halu Oleo, INDONESIA

2. Department of Agriculture, Graduate Program, Universitas Halu Oleo, INDONESIA

Abstract

A closed interaction of predator prey is considered. The interaction is expressed in the Lotka-Volterra model. Two types of Lotka-Volterra models are considered, with and without carrying capacity of the prey. The paper includes a periodic harvesting of predator and/or prey, a function of time which acts to the model. Hence, the model is in the form of a system of non-homogeneous equations. Dynamical properties of the models are investigated. The solutions are computed numerically. Such interaction is in the need of integrated farming on harvesting of predator and/or prey. In this model the number of population in the system is sensitive to the initial value, which can be applied to the integrated farming systems such that the system remains sustainable.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

Computer Science Applications,Control and Systems Engineering

Reference23 articles.

1. A. J. Lotka, Contribution to the theory of periodic reactions, Journal of Physical Chemistry, vol. 14, no. 3, 1910, pp. 271–274.

2. V. Volterra, Variations and fluctuations of the number of individuals in animal species living together, ICES Journal of Marine Science, vol. 3, no. 1, 1928, pp. 3–51.

3. D. Zwillinger, Handbook of Differential Equations, 3rd ed. Boston: Academic Press, 1997.

4. D. K. Arrowsmith and C. M. Place, An Introduction to Dynamical Systems. Cambridge University Press, 1990.

5. W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 7th ed. New York: John Wiley & Sons, Inc, 2000.

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