Hopf bifurcation and period functions for Wright type delay differential\n equations

2018/01/12 by István Balázs, Balázs, István, Gergely Röst +1
Mathematics · Computer Science · Medicine · #Advanced Differential Equations and Dynamical Systems #Nonlinear Dynamics and Pattern Formation #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1801.04325

Abstract

We present the simplest criterion that determines the direction of the Hopf\nbifurcations of the delay differential equation x'(t)=-\μ f(x(t-1)), as the\nparameter \μ passes through the critical values \μ_k. We give a complete\nclassification of the possible bifurcation sequences. Using this information\nand the Cooke-transformation, we obtain local estimates and monotonicity\nproperties of the periods of the bifurcating limit cycles along the\nHopf-branches. Further, we show how our results relate to the often required\nproperty that the nonlinearity has negative Schwarzian derivative.\n

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