Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators

<div>Phase portrait for homoclinic solutions of (<a href="https://static.hindawi.com/articles/sv/volume-2016/9471423/figures/#EEq56">48</a>): — AUTO numerical method [<a href="/journals/sv/2016/9471423/#B30">30</a>, <a href="/journals/sv/2016/9471423/#B31">31</a>]; ○○○ present method; <svg height="7.35473pt" id="M138" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 23.0785 7.35473" width="23.0785pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.631,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,15.291,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g></svg> generalized harmonic function perturbation method [<a href="/journals/sv/2016/9471423/#B20">20</a>].</div>

Shock and Vibration

fig4

Figure 4

Figure 4: Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators 