Global dynamics of delay differential equations

AbstractIn this survey paper the delay differential equation $$ \dot x(t) = - \mu x(t) + g(x(t - 1)) $$(t) = −µx(t) + g(x(t − 1)) is considered with µ ≥ 0 and a smooth real function g satisfying g(0) = 0. It is shown that the dynamics generated by this simple-looking equation can be very rich. The dynamics is completely understood only for a small class of nonlinearities. Open problems are formulated.

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