i-manager Publications

Mathematical Analysis of One Ammensal and Two Mutualistic Species

N. V. S. R. C. Murty Gamini*, Paparao A. V.**

* Department of Science & Humanities, BVC Institute of Technology & Science, Amalapuram, Andhra Pradesh, India.

** Department of Mathematics, JNTUK University College of Engineering, Vizianagaram, Andhra Pradesh, India.

Periodicity:October - December'2019
DOI : https://doi.org/10.26634/jmat.8.4.17131

Abstract

In this paper we studied the dynamics of one ammensal and two mutualistic species. A distributed time lag is induced in the interaction of ammensal and two mutual species. Local and global stability analysis is discussed at co-existing state. Numerical simulation with different delay kernel strengths are illustrated and proved that delay kernels play a significant role in the growth of two mutual species populations.

Keywords

Ammensal, Mutualism, Co-existing state, Stability, Delay Kernels.

How to Cite this Article?

Gamini, N. V. S. R. C. M., and Paparao, A. V. (2019). Mathematical Analysis of One Ammensal and Two Mutualistic Species. i-manager's Journal on Mathematics, 8(4), 19-31. https://doi.org/10.26634/jmat.8.4.17131

References

[1]. Alfred, J. (1925). Elements of physical biology. Baltimore, London: Williams and Wilkins.

[2]. Cushing, J. M. (1977). Integro-Differential equations and delay models in population dynamics. Verlag, Heidelberg: Springer.

[3]. Freedman, H. I. (1980). Deterministic mathematical models in population ecology. New York: Marcel Dekker Incorporated.

[4]. Kapur, J. N. (1988). Mathematical Modeling. New Delhi: Wiley-Eastern Limited.

[5]. Kapur, J. N. (1985). Mathematical models in biology and medicine. New Delhi: Affiliated East-West Press.

[6]. May, R. M. (1973). Stability and complexity in model Eco-Systems. (Vol. 1). Princeton: Princeton University Press.

[7]. Narayan, L. K., & Rao, K. K. (2016). Stability Analysis of a Three Species Syn-Ecological Model with Prey-Predator and Amensalism. Bulleten of Calcutta Mathematical Society, 108(1), 63-76.

[8]. Narayan, L. K., & Rao, K. K. (2017). Dynamical System of Ammensal Relationship of Human's on Plants and Birds with Time Delay. Bulletin of Calcutta Mathematical Society, 109(6), 485-500.

[9]. Narayan, L. K., & Rao, K. K. (2017). Stability Analysis of Three Species Food Chain Model with Ammensalism and Mutualism. In Proceedings of the 11th International Conference MSAST 2017 (IMBIC) Kolkata, 6, 125-135.

[10]. Paparao A. V., & Gamini, N. V. S. R. C. M. (2018). Dynamical Behaviour of Prey Predators Model with Time Delay. International Journal of Mathematics And its Applications, 6(3), 27-37.

[11]. Paparao, A. V., & Narayan, K. L. (2017). Dynamics of a prey predator and competitor model with time delay. International Journal of Ecology & Development, 32(1), 75-86.

[12]. Paparao, A. V., & Narayan, K. L. (2017). A prey, predator and a competitor to the predator model with time delay. International Journal of Research in Science & Engineering, 27-38.

[13]. Paparao, A. V., Narayan. K. L., & Rao, K. K. (2019). Amensalism Model: A Mathematical Study. International Journal of Ecological Economics & Statistics (IJEES), 40(3), 75-87.

[14]. Rao, V. S. H., & Rao, P. R. S. (2009). Dynamic models and control of biological systems. Verlag, New York: Springer.

[15]. Voltera, V. (1931). Leçons sur la théorie mathématique de la Lutte pour la vie (Lessons on the Mathematical Theory of Struggle for Life). Paris: Gauthier Villars.

If you have access to this article please login to view the article or kindly login to purchase the article

Single Article

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Online	15	15

ADD TO CART

Options for accessing this content:

If you would like institutional access to this content, please recommend the title to your librarian.
If you already have i-manager's user account: Login above and proceed to purchase the article.
New Users: Please register, then proceed to purchase the article.