Competition among Predators and Allee Effect on Prey, Their Influence on a Gause-Type Predation Model. (21st March 2019)

• Record Type: Journal Article
• Authors: González-Olivares, Eduardo; Cabrera-Villegas, Javier; Córdova-Lepe, Fernando; Rojas-Palma, Alejandro
• Other Names: Naddeo Alessandro Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2019(2019)
• Publication Date: 2019-03-21
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2019/3967408
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Interference or competition among predators (CAP) has often been ruled out in depredation models, although there are varied mathematical forms to describe and incorporate it into this interaction. In this work, we present the most known of these descriptions and one of them will be used in a modified Volterra model. Moreover, of this ecological phenomenon, a simple and strong Allee effect affecting the prey population will be considered in the relationship. An important feature of the new model is to have until two positive equilibrium points, to the difference with the Volterra model (without Allee effect); hence different and interesting dynamic situations appear in the system. Conditions for the existence and local stability of equilibria are determined. The boundedness of solutions, the existence of a limit cycle and a separatrix curve are also proven. Besides, the main properties of the model are examined from an ecological point of view. To make a comparative discussion of our results, an Appendix is added with the main properties of models, in which neither the Allee effect nor the competition among predators is considered. Some simulations are shown to endorse our results.