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.008a" src="https://static.hindawi.com/articles/aaa/volume-2014/545236/figures/545236.fig.008a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Bifurcation diagram for <svg height="11.175" id="M235" 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.008b" src="https://static.hindawi.com/articles/aaa/volume-2014/545236/figures/545236.fig.008b.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 for <svg height="15.95" id="M233" 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>
<g transform="matrix(.012,-0,0,-.012,9.738,15.888)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g>
<g transform="matrix(.017,-0,0,-.017,21.875,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,36.562,10.862)"><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>
</svg>, <svg height="15.95" id="M234" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 46.012501 15.95" width="46.012501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><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,-.012,9.738,15.888)"><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,-.017,23.088,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,37.774,10.862)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>.</table>

Abstract and Applied Analysis

fig8

Figure 8

Figure 8: Equilibrium Point Bifurcation and Singularity Analysis of HH Model with Constraint 