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Negativity of delayed induced oscillations in a simple linear DDE. (English) Zbl 1218.34079
Oscillatory behaviour appearing in the equation
\[ \frac{dx}{dt} = A-Bx(t)-Cx(t-\tau) \]
with \(B < C\) and \(\tau \geq (c^2-B^2)^{-1/2}\cos^{-1}(-B/C)\) is studied. It is shown that, for a solution with \(x(s)=0\) for \(s<0\) and \(x(0)=x^0\geq 0\), and some other initial values, there exists always a \(t\in (0, 4\tau)\) such that \(x(t)<0\). This shows that the proposed Cauchy problem is not a proper description of biochemical reactions or of other biological and physical quantities.

34K11 Oscillation theory of functional-differential equations
34K06 Linear functional-differential equations
Full Text: DOI
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