Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

<div class="floats-full-page floats-full-page-figure"><h2>Figure 3</h2><div class="floats-full-page-caption"><table>Bifurcation diagram of system (<a href="../../478315/#EEq1.4">4</a>) near <svg height="15.25" id="M498" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 18.5375 15.25" width="18.5375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M619 482q0 -69 -40.5 -119t-96 -72.5t-118.5 -26.5h-44l-70 20l-31 -151q-14 -67 0.5 -83t89.5 -22l-5 -28h-287l8 28q65 7 81.5 22t29.5 83l79 398q12 56 0.5 70.5t-78.5 20.5l7 28h255q108 0 164 -43t56 -125zM524 478q0 141 -146 141q-25 0 -47 -8q-16 -6 -20.5 -13.5&#10;t-10.5 -39.5l-43 -241q37 -13 83 -13q67 0 125.5 45t58.5 129z" id="x1D443"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><path d="M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5&#10;q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z" id="x2217"></path></g>
</svg> in the plane of <svg height="12.775" id="M499" style="vertical-align:-4.0404pt" version="1.1" viewbox="0 0 15.8875 12.775" width="15.8875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M538 96q-38 -45 -84 -76.5t-71 -31.5q-44 0 -15 117q12 49 18 89h-2q-99 -128 -163 -178q-36 -28 -70 -28q-26 0 -44 38h-2q-16 -69 -16 -129q0 -43 11 -75.5t24 -42.5l1 -6q-7 -12 -24.5 -23t-37.5 -11q-40 0 -40 76q0 52 35 202l94 407l78 24l5 -5q-32 -122 -72 -310&#10;q-7 -33 0 -55t25 -22q36 0 105.5 75t107.5 145l32 146l75 26h10q-50 -197 -78 -347q-7 -38 6 -38q7 0 31 17t47 39z" id="x1D707"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.5,12.713)"><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> and <svg height="12.775" id="M500" style="vertical-align:-4.0404pt" version="1.1" viewbox="0 0 15.8875 12.775" width="15.8875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M538 96q-38 -45 -84 -76.5t-71 -31.5q-44 0 -15 117q12 49 18 89h-2q-99 -128 -163 -178q-36 -28 -70 -28q-26 0 -44 38h-2q-16 -69 -16 -129q0 -43 11 -75.5t24 -42.5l1 -6q-7 -12 -24.5 -23t-37.5 -11q-40 0 -40 76q0 52 35 202l94 407l78 24l5 -5q-32 -122 -72 -310&#10;q-7 -33 0 -55t25 -22q36 0 105.5 75t107.5 145l32 146l75 26h10q-50 -197 -78 -347q-7 -38 6 -38q7 0 31 17t47 39z" id="x1D707"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.5,12.713)"><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></div><div class="floats-full-page-content"><table class="table-group" width="800px"><tr class="fig-image"><td><img alt="478315.fig.003" src="https://static-01.hindawi.com/articles/aaa/volume-2013/478315/figures/478315.fig.003.jpg" /></td></tr></table></div></div>

Figure 3 | Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

title

Figure 3: Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

description

Figure 3

About this journal

<p><em>Abstract and Applied Analysis</em> publishes research with an emphasis on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimisation theory, and control theory.</p>


Journal profile

Meet the editorial board

<p>Chief Editor, Dr Wong, is an associate professor at Nanyang Technological University, Singapore. Her research interests include differential equations, difference equations, integral equations, and numerical mathematics.</p>


Editor spotlight

Submit your proposal

Do you think there is an emerging area of research that really needs to be highlighted? Or an existing research area that has been overlooked or would benefit from deeper investigation? Raise the profile of a research area by leading a Special Issue.