Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos

<table>When <svg height="13.1625" id="M280" style="vertical-align:-1.59705pt" version="1.1" viewbox="0 0 99.037498 13.1625" width="99.037498" 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)"><use xlink:href="#x1D43E"></use></g><g transform="matrix(.017,-0,0,-.017,17.962,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,32.666,11.112)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,42.644,11.112)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,50.804,11.112)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,63.179,11.112)"><use xlink:href="#x1D70F"></use></g><g transform="matrix(.017,-0,0,-.017,76.115,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,90.819,11.112)"><use xlink:href="#x32"></use></g>
</svg>, chaos vanishes, and <svg height="15.5375" id="M281" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 14.6125 15.5375" width="14.6125" 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)"><use xlink:href="#x1D446"></use></g>
<g transform="matrix(.012,-0,0,-.012,8.225,15.475)"><use xlink:href="#x32"></use></g>
</svg> becomes a stable periodic solution. Here initial value is <svg height="15.0875" id="M282" style="vertical-align:-2.3205pt" version="1.1" viewbox="0 0 71.099998 15.0875" width="71.099998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,5.944,12.138)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,14.103,12.138)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,26.462,12.138)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,36.44,12.138)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,44.599,12.138)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,56.974,12.138)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,65.134,12.138)"><use xlink:href="#x29"></use></g>
</svg>.</table>

Journal of Applied Mathematics

fig6

Figure 6

Figure 6: Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos 