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Start Over Subject delay differential equation

1. Convergence to equilibria in a differential equation with small delay

Creator:
Pituk, Mihály
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
delay differential equation, equilibrium, and convergence
Language:
English
Description:
Consider the delay differential equation (1) ˙x(t) = g(x(t), x(t − r)), where r > 0 is a constant and g : 2 → is Lipschitzian. It is shown that if r is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Time delay in chemical exchange during an NMR pulse

Creator:
Gamliel, Dan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
magnetic resonance, spin exchange, delay differential equation, and characteristic equation
Language:
English
Description:
Spin exchange with a time delay in NMR (nuclear magnetic resonance) was treated in a previous work. In the present work the idea is applied to a case where all magnetization components are relevant. The resulting DDE (delay differential equations) are formally solved by the Laplace transform. Then the stability of the system is studied using the real and imaginary parts of the determinant in the characteristic equation. Using typical parameter values for the DDE system, stability is shown for all relevant cases. Also non-oscillating terms in the solution were found by studying the same determinant using similar parameter values.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public