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Secondly, the impact of the time delay on the stability of the delay differential equation (DDE) model is investigated, where time delay is regarded as a bifurcation parameter.
Differing from the first route, Jackson et al. also devised another electronic device to produce STDP where time delay is internally determined by a simple RC circuit [94], as revealed in Fig. 20.
For the sake of simplicity and since the case where time delay exists in the function "g" has been already studied before (at least for some types of delays) we shall focus on the distributed delay present in the nonlinearity "f ".
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For this, we present a two-stage coordinate transformation method to transform any given time-delay system into an observable canonical form where time delays appear in the input and output vectors, but not in the state vector.
Further, we show that the permanence and extinction of the discrete system (3.1) are equivalent to their corresponding continuous systems (see [40, 43, 45]), where time delays are also both harmless for the permanence and profitless to the extinction of species of the system.
These voltages were controlled by power supplies triggered by the opening of the exit ion gate in the ion funnel trap, where time delays and pulse widths can be controlled using in-house developed instrument control software.
4 Ward et al 5 identified periods during the sequence of events where time delays were unacceptable (mainly ECG to exit emergency room (ER) and sheath to balloon inflation) and they made changes in their local guidelines for STEMI that reduced door-to-balloon times from 136 to 82 min.
The system is permanent when (T=0.8>T_{2}^) where the time delay (tau=0.5,0.7,3,6), respectively (see Figure 4).
In this work we explore a system where a time delay can be both stabilizing and destabilizing.
Then, the predator-extinction periodic solution is globally attractive when (T=0.5< T_{1}^) (see Figure 2 (right) and Figure 3 (right)) where the time delay (tau=0.5,0.7,3,6), respectively.
The pole placement method together with LQR is ingeniously used for SOPTD systems where the time delay part is handled in the controller output equation instead of characteristic equation.
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