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Periodic dynamics in a model of immune system. (English) Zbl 1007.34067
Summary: The authors study periodic solutions to Marchuk’s model, i.e. the system of ordinary differential equations with time delay describing immune reactions. The Hopf bifurcation theorem is used to show the existence of a periodic solution for some values of the delay. Periodic dynamics caused by periodic immune reactivity or periodic initial data functions are compared. Autocorrelation functions are used to check the periodicity or quasiperiodicity of the behaviour.

34K13 Periodic solutions to functional-differential equations
92C30 Physiology (general)
Full Text: DOI EuDML