Temporal Response of Predator-Prey System with the Allee Effect

Year 2020, , 54 - 65, 28.06.2020

Yadigar Sekerci

https://doi.org/10.35193/bseufbd.648992

Abstract

Temporal dynamics of a predator-prey model, in which predator mortality rate varies linearly in time, is considered with the assumption that prey growth is stressed by the strong Allee effect. In this work, temporal structure of prey-predator system consisting of two coupled ordinary differential equations is examined. By means of extensive numerical simulations it is shown that the system has rich temporal structure and the system can be stabilizes with the change in predator mortality rate. Obtained results show that with an increasing stress on prey due to Allee affect and the increase in predator population size, the system push the prey to extinct and then the system is extinct due to absence of prey for predator.

Keywords

Predator-Prey system, Allee Effect, Mathematical Modelling

Supporting Institution

Amasya Universitesi

Project Number

FBM-BAP 17-0258

Thanks

This research has been supported by Amasya University Scientific Research Projects Coordination Unit. Project Number: FBM-BAP 17-0258.

Allee Etkisi Altındaki Av-Avcı Sisteminin Zamana Bağlı Değişimi

Abstract

Allee etkisi altındaki avın büyüme katkısının baskılandığı ve avcı ölüm oranının zaman içinde doğrusal olarak değiştiği av-avcı modelinin zamana bağlı dinamikleri ele alınmıştır. Bu çalışmada, av-avcı sisteminin zamana bağlı dinamik yapısı ikili adi diferansiyel denklem ile incelenmiştir. Çok sayıdaki nümerik simülasyonlar sayesinde sistemin çeşitli zamansal yapıya sahip olduğu ve sistemin avcının ölüm katsayısındaki değişim ile dengelenebileceği gösterilmiştir. Elde edilen sonuçlar göstermektedir ki Allee etkisi altında ve avcı popülasyonunun artmasıyla birlikte av üzerindeki baskının artması ile system, avı neslinin tükenmesine zorlamıştır ve dolayısıyla avın olmaması avcının neslini de tüketmiştir.

Keywords

Av-Avcı Sistemi, Allee Etkisi, Matematiksel Modelleme

Project Number

FBM-BAP 17-0258

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