On the Number of Limit Cycles of a Piecewise Quadratic Near-Hamiltonian System

<div>Phase portrait of system (<a href="https://static.hindawi.com/articles/aaa/volume-2014/385103/figures/#EEq1.1">1</a>)<svg height="13.1057pt" id="M79" style="vertical-align:-3.427799pt" version="1.1" viewbox="-0.0498162 -9.6779 18.6245 13.1057" width="18.6245pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M162 -163V703H101V-163H162Z" id="g113-9"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,3.563,3.264)"><path d="M396 374C396 399 365 451 262 451C173 451 84 405 84 327C84 295 107 257 157 243V241C91 226 24 184 24 119C24 41 92 -12 189 -12C272 -12 344 31 386 91L367 118C325 76 274 50 222 50C163 50 120 84 120 138C120 191 169 218 223 218C247 218 263 217 278 216L312 260L308 267H259C200 267 167 297 167 338S202 414 250 414C297 414 326 387 336 341C338 331 341 328 349 328C361 328 396 349 396 374Z" id="g50-247"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="420" vert-adv-y="420"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,7.547,3.264)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,13.342,3.264)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> under (<a href="https://static.hindawi.com/articles/aaa/volume-2014/385103/figures/#EEq2.3">9</a>).</div>

Abstract and Applied Analysis

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Figure 3

Figure 3: On the Number of Limit Cycles of a Piecewise Quadratic Near-Hamiltonian System 