Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System

<table>The stable periodic orbits of system (<a href="https://static-preview.hindawi.com/articles/jam/volume-2012/260798/figures/#EEq3">1.6</a>) when <svg height="11.125" id="M284" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 88.75 11.125" width="88.75" 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)"><use xlink:href="#x1D70F"></use></g><g transform="matrix(.017,-0,0,-.017,12.982,10.862)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,27.685,10.862)"><use xlink:href="#x34"></use></g><g transform="matrix(.017,-0,0,-.017,35.845,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,44.004,10.862)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,52.164,10.862)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,56.039,10.862)"><use xlink:href="#x37"></use></g><g transform="matrix(.017,-0,0,-.017,64.199,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,72.358,10.862)"><use xlink:href="#x38"></use></g><g transform="matrix(.017,-0,0,-.017,80.518,10.862)"><use xlink:href="#x38"></use></g>
</svg> and <svg height="11.175" id="M285" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 88.75 11.175" width="88.75" 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)"><use xlink:href="#x1D70F"></use></g><g transform="matrix(.017,-0,0,-.017,12.982,10.862)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,27.685,10.862)"><use xlink:href="#x38"></use></g><g transform="matrix(.017,-0,0,-.017,35.845,10.862)"><use xlink:href="#x39"></use></g><g transform="matrix(.017,-0,0,-.017,44.004,10.862)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,52.164,10.862)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,56.039,10.862)"><use xlink:href="#x37"></use></g><g transform="matrix(.017,-0,0,-.017,64.199,10.862)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,72.358,10.862)"><use xlink:href="#x38"></use></g><g transform="matrix(.017,-0,0,-.017,80.518,10.862)"><use xlink:href="#x38"></use></g>
</svg> with parameters given by (3).</table>

Journal of Applied Mathematics

fig4

Figure 4

Figure 4: Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System 