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.008a" src="https://static.hindawi.com/articles/jam/volume-2014/823937/figures/823937.fig.008a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Simulation results with <svg height="11.125" id="M308" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 62.487499 11.125" width="62.487499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,47.88,10.862)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,56.039,10.862)"><path d="M352 391q0 -31 -27 -44q-14 -7 -24 6q-39 48 -84 48q-23 0 -39.5 -15t-16.5 -40q0 -43 73 -90q49 -32 70 -58t21 -57q0 -58 -62 -105.5t-129 -47.5q-40 0 -75.5 25t-35.5 52q0 28 32 46q7 4 15 3t11 -6q19 -31 48.5 -50.5t54.5 -19.5q34 0 54 19.5t20 42.5q0 43 -65 81
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</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="823937.fig.008b" src="https://static.hindawi.com/articles/jam/volume-2014/823937/figures/823937.fig.008b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Simulation results with <svg height="11.125" id="M310" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 62.487499 11.125" width="62.487499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<table>Simulation results with various <svg height="8.125" id="M307" 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
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</svg> values.</table>

Journal of Applied Mathematics

fig8

Figure 8

Figure 8: A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag 