![]() Leslie PH (1948) Some further notes on the use of matrices in population mathematics. Kendall BE (2001) Nonlinear dynamics and chaos, eLS 13: 255–263 Jana A, Roy SK (2022) Holling-Tanner prey-predator model with Beddington-DeAngelis functional response including delay. Hunsicker ME, Cianelli L, Bailey KM, Buckel JA et al (2011) Functional responses and scaling in predator–prey interactions of marine fishes: contemporary issues and emerging concepts. Holling CS (1959) Some characteristics of simple types of predation and parasitism. ![]() Society for Industrial and Applied Mathematics, Philadelphia Haberman R (1998) Mathematical models mechanical vibrations, population dynamics, and traffic flow. Gakkhar S, Singh B, Naji RK (2007) Dynamical behavior of two predators competing over a single prey. Gakkhar S, Naji RK (2003) Seasonally perturbed prey–predator system with predator-dependent functional response. įreedman I (1980) Deterministic mathematical models in population ecology. J North Am Benthol Soc 8:211–221ĭeAngelis DL, Goldsten RA, O’Neill RV (1975) A model for trophic interaction. Ecol Lett 5:302–315Ĭrowley PH, Martin EK (1989) Functional responses and interference within and between year classes of a dragonfly population. Ĭhase RD, Abrams PA, Grover J, Diehl S, Holt RD, Richards S, Case T, Wilson W, Nisbet R, Chesson P (2002) The influence between predation and competition a review and synthesis. J Appl Math Comput 43:271–293īeddington JR (1975) Mutual interference between parasites or predators and its effect on searching efficiency. Īli N, Jazar M (2013) Global dynamics of a modified Leslie-Gower predator–prey model with Crowley–Martin functional responses. In: Proceedings of the 2012a International Conference on Statistics in Science, Business and Engineering, Langkawi, Malaysia, 10–a. Īlebraheem J, Abu-Hassan Y (2012a) Simulation of complex dynamical behaviour in prey predator model. Res J Appl Sci 8:286–295Īlebraheem J, Abu-Hassan Y (2014) Dynamics of a two predator–one prey system. J Appl Sci 6:943–956Īlebraheem J, Abu-Hassan Y (2013) Efficient biomass conversion and its effect on the existence of predators in a predator–prey system. J Appl Sci 11:3717–3724Īlebraheem J, Abu-Hassan Y (2012b) Persistence of predators in a two predators–one prey model with non-periodic solution. ![]() Īlebraheem J, Abu-Hassan Y (2011) The effects of capture efficiency on the coexistence of a predator in a two predators–one prey model. Symmetry 10:532Īlebraheem J (2021) Dynamics of a predator–prey model with the effect of oscillation of immigration of the prey. Sci Int 28:2357–2362Īlebraheem J (2018) Relationship between the paradox of enrichment and the dynamics of persistence and extinction in prey–predator systems. Īlebraheem J (2016) Fluctuations in interactions of prey predator systems. ![]() ![]() Our approach gives good correspondence between an important real data and computer simulations.Ību-Hasan Y, Alebraheem J (2015) Functional and numerical response in prey–predator system. The novel approach is explained for the mechanism measurement of predator interference through depending on numerical response. We consider a predator–prey model and a two-predator one-prey model to explain the idea. Our aim is to clarify the relationship between models and Holling types functional and numerical responses in order to gain insights into predator interferences and to answer an important question how competition is carried out. In this paper, the two populations’ growth rates obey the logistic law and the carrying capacity of the predator depends on the available number of prey are considered. The main components of any predator–prey models are, firstly, how the different population classes grow and secondly, how the prey and predator interacts. Various mathematical models have made considerable contributions in gaining a better understanding of the predator–prey interactions. A characteristic of ecosystems is the existence of manifold of independencies which are highly complex. ![]()
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