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Journal of Applied Nonlinear Dynamics 9(1) (2020) 37--46 | DOI:10.5890/JAND.2020.03.004

Jair Silvério Dos Santos

Departamento de Computação e Matemática, Faculdade de Filoso a, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Br

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Abstract

This paper is concerned with the dynamics of the steady state twodelayed models when the involved functions describe the saturation effect whereby the prey density increases, the predation rate becomes less dependent on the population of the prey and only ependent on the predator population. The stability of the steady state together with its dependence on the magnitude of time delays is examined and by means Hopf-bifurcation theory it is showed that a generator of selfsustaining cycles appear. The normal form is applied to determine the direction of the bifurcation and the stability of the periodic orbits bifurcating from a steady state. This paper is dedicated to Albino and Conceição.

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