Dynamics of a Host-Parasitoid Model Related to Pennycuick Growth Form

Yıl 2019, Cilt: 2 Sayı: 4, 170 - 179, 26.12.2019

Özlem Ak Gümüş , Bekir Sıtkı Bilgi

https://doi.org/10.32323/ujma.561690

Cited By: 1

Öz

In this study, the dynamical results of the model by obtaining the steady states existing in the host-parasitoid model were given. Also, some results relating to steady states of the model by depending the parameter made from biological assumptions were obtained.

Anahtar Kelimeler

Discrete-time system, Host-parasitoid model, Stability, Steady state, Nicholson Bailey model, Pennycuick form

Kaynakça

• [1] A. Nicholson and V. Bailey, The balance of animal population, Proc. Zool. Soc. Lond., 3, (1935).
• [2] L.J.S. Allen, An Introduction to Mathematical Biology, Pearson, New Jersey, (2007).
• [3] Ö . Ak Gümüş, Dynamical Consequences and Stability Analysis of a New Host-Parasitoid Model, Gen. Math. Notes, 27(1), (2015), 9-15.
• [4] Ö . Ak Gümüş, Kangalgil F., Allee effect and stability in a discrete-time host-parasitoid model, J. Adv. Res. Appl. Math., 7(1), (2015), 94-99.
• [5] U. Ufuktepe, S. Kapc¸ak, Stability analysis of a host parasite model, Adv. Differ. Equ. doi:10.1186/1687-1847-2013-79.
• [6] M. N. Qureshi, A. Q. Khan and Q. Din, Asymptotic behavior of a Nicholson-Bailey model, 62, (2014), doi:10.1186/1687-1847.
• [7] A. Q. Khan and M. N. Qureshi, Dynamics of a modified Nicholson-Bailey host-parasitoid model, Adv. Difference Equ., 23, (2015), doi:10.1186/s13662- 015-0357-2.
• [8] W. C. Allee Animal Aggregations: A Study in General Sociology, University of Chicago Press, Chicago (1931).
• [9] U. Ufuktepe, S. Kapc¸ak S and O. Akman, Stability analysis of the Beddington model with Allee effect, Appl. Math. Inf. Sci. 9, (2015), 603-608.
• [10] C. J. Pennycuick, R. M. Compton and A. Beckingham, A Computer Model for Simulating the Growth of a Population, or of Two Interacting Populations, J. Theoret. Biol., 18, (1968), 316-329.