Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input

<table>Time series of  <svg height="16.625" id="M387" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 27.525 16.625" width="27.525" 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)"><path d="M556 393q0 -39 -36 -106q-42 -78 -185 -279q-47 -66 -81 -108t-117 -135l-112 -26l-8 22q150 90 251 219q-6 136 -39 340q-8 53 -21 53q-6 0 -27 -19.5t-38 -42.5l-16 26q80 111 127 111q23 0 35 -28t20 -90q18 -137 27 -263h2q142 200 142 279q0 24 -14 48q-4 7 5 26
q13 28 43 28q18 0 30 -15.5t12 -39.5z" id="x1D466"></path></g><g transform="matrix(.017,-0,0,-.017,9.905,12.138)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,15.786,12.138)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g><g transform="matrix(.017,-0,0,-.017,21.583,12.138)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg>.</table>

Discrete Dynamics in Nature and Society

fig2

Figure 2

Figure 2: Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input 