Bifurcation of Nongeneric Homoclinic Orbit  Accompanied by Pitchfork  Bifurcation

<table>Homoclinic orbit with <svg height="11.75" id="M206" style="vertical-align:-0.23206pt" version="1.1" viewbox="0 0 13.175 11.75" width="13.175" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M745 361q0 -166 -116 -272t-291 -106q-136 0 -225.5 83t-89.5 218q0 161 115.5 272t288.5 111q137 0 227.5 -83t90.5 -223zM643 359q0 126 -56 199.5t-167 73.5q-130 0 -213.5 -104t-83.5 -246q0 -117 58 -190.5t165 -73.5q91 0 160.5 52t103 128.5t33.5 160.5z" id="x1D442"></path></g>
</svg>.</table>

Abstract and Applied Analysis

fig2

Figure 2

Figure 2: Bifurcation of Nongeneric Homoclinic Orbit  Accompanied by Pitchfork  Bifurcation 