A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="823937.fig.0012a" src="https://static.hindawi.com/articles/jam/volume-2014/823937/figures/823937.fig.0012a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Real parts of two eigenvalues with <svg height="8.125" id="M338" style="vertical-align:-0.0627pt" version="1.1" viewbox="0 0 8.3374996 8.125" width="8.3374996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.863)"><path d="M471 456q-22 -60 -37 -85q-20 -3 -84 -3q-9 0 -29 2t-29 2q-38 -145 -54 -234q-15 -80 14 -80q23 0 68 38l14 -25q-78 -83 -137 -83q-50 0 -50 64q0 25 7 57l67 266q-57 4 -98 -9t-80 -49l-20 21q14 18 27 31t36.5 30t56.5 26t73 9q26 0 82.5 -2t89.5 -2q21 0 32 5t24 24
z" id="x1D70F"></path></g>
</svg> increasing</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="823937.fig.0012b" src="https://static.hindawi.com/articles/jam/volume-2014/823937/figures/823937.fig.0012b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Imaginary parts of two eigenvalues with <svg height="8.125" id="M339" style="vertical-align:-0.0627pt" version="1.1" viewbox="0 0 8.3374996 8.125" width="8.3374996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.863)"><path d="M471 456q-22 -60 -37 -85q-20 -3 -84 -3q-9 0 -29 2t-29 2q-38 -145 -54 -234q-15 -80 14 -80q23 0 68 38l14 -25q-78 -83 -137 -83q-50 0 -50 64q0 25 7 57l67 266q-57 4 -98 -9t-80 -49l-20 21q14 18 27 31t36.5 30t56.5 26t73 9q26 0 82.5 -2t89.5 -2q21 0 32 5t24 24
z" id="x1D70F"></path></g>
</svg> increasing</td></tr></table></td></tr></table>

<table>Real and imaginary parts of two eigenvalues.</table>

Journal of Applied Mathematics

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Figure 12

Figure 12: A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag 