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Solution multistability in first-order nonlinear differential delay equations. (English) Zbl 1055.34510

Summary: The dependence of solution behavior to perturbations of the initial function (IF) in a class of nonlinear differential delay equations (DDEs) is investigated. The structure of basins of attraction of multistable limit cycles is investigated. These basins can possess complex structure at all scales measurable numerically although this is not necessarily the case. Sensitive dependence of the asymptotic solution to perturbations in the initial function is also observed experimentally using a task specific electronic analog computer designed to investigate the dynamics of an integrable first-order DDE.

MSC:

34K20 Stability theory of functional-differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34K18 Bifurcation theory of functional-differential equations
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