Equilibrium Point Bifurcation and Singularity Analysis of HH Model with Constraint

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="545236.fig.003a" src="https://static.hindawi.com/articles/aaa/volume-2014/545236/figures/545236.fig.003a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Bifurcation diagram for <svg height="11.175" id="M74" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 7.5500002 11.175" width="7.5500002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M414 650l-6 -28q-63 -4 -78.5 -17.5t-27.5 -71.5l-77 -416q-11 -58 0.5 -71.5t77.5 -17.5l-5 -28h-275l8 28q63 4 79.5 18.5t27.5 70.5l80 416q11 57 -2 71t-81 18l6 28h273z" id="x1D43C"></path></g>
</svg> variation</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="545236.fig.003b" src="https://static.hindawi.com/articles/aaa/volume-2014/545236/figures/545236.fig.003b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Stability of equilibrium points</td></tr></table></td></tr></table>

<table>The bifurcation diagram and stability of equilibrium points for <svg height="15.95" id="M72" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 44.799999 15.95" width="44.799999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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t-20.5 85q0 74 32.5 145.5t84.5 117.5q40 35 100 58.5t117 23.5q21 0 65 -8q30 -6 44 -6zM456 386q-40 16 -81 16q-29 0 -64 -13q-42 -17 -85 -97q-19 -36 -31.5 -86t-12.5 -86q0 -64 30 -64q20 0 52.5 21t60.5 52q74 81 95 123q26 62 36 134z" id="x1D454"></path></g>
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<g transform="matrix(.017,-0,0,-.017,.062,10.8)"><path d="M546 430q-14 -33 -37.5 -140t-38.5 -209q-29 -195 -156 -289q-29 -21 -70 -37t-78 -16q-62 0 -102.5 37t-40.5 69q0 27 26 48q19 15 25 -3q13 -43 46.5 -69t87.5 -26q55 0 83 21q29 22 50 65t43 140q14 64 29 163h-2q-55 -81 -149 -152q-59 -44 -102 -44q-23 0 -43.5 30
t-20.5 85q0 74 32.5 145.5t84.5 117.5q40 35 100 58.5t117 23.5q21 0 65 -8q30 -6 44 -6zM456 386q-40 16 -81 16q-29 0 -64 -13q-42 -17 -85 -97q-19 -36 -31.5 -86t-12.5 -86q0 -64 30 -64q20 0 52.5 21t60.5 52q74 81 95 123q26 62 36 134z" id="x1D454"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.738,15.838)"><path d="M667 0h-153l-248 291q-28 32 -54 27v-190q0 -65 14.5 -80t77.5 -20v-28h-260v28q58 5 71 20t13 80v392q0 48 -6 66.5t-22 25.5t-59 10v28h258v-28q-59 -5 -73 -20.5t-14 -81.5v-175q29 6 70 45q101 97 167 178q23 27 20 37t-36 14l-23 3v28h240v-28q-57 -5 -86 -18.5
t-76 -56.5q-40 -35 -177 -175q97 -124 235 -272q39 -41 61.5 -54t59.5 -18v-28z" id="x4B"></path></g>
<g transform="matrix(.017,-0,0,-.017,23.088,10.8)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,37.774,10.8)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg>.</table>

Abstract and Applied Analysis

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Figure 3

Figure 3: Equilibrium Point Bifurcation and Singularity Analysis of HH Model with Constraint 