2023/06/14 by A. Gómez, Gomez, Adrian, José Oyarce +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #34C20 #34K13 #34K18 #34K20 #92D25 #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2306.08755
openalex publication_date 2023/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the scalar autonomous equation with two discrete delays x(t)=f(x(t),x(t-r),x(t-σ)), where f:ℝ3→ ℝ is a continuously differentiable non-linear function such that f(0,0,0)=0. It is shown that if the difference between the delays is constant, then one of the delays becomes a Hopf-bifurcation parameter and, in addition, the absolute stability of the trivial solution can be established. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using normal form theory. The main results are applied to guarantee the existence of positive periodic solutions to Nicholson's blowflies and Mackey-Glass models, both with a delayed harvesting term. The conclusions are illustrated by numerical simulations.