Complex Dynamical Behaviors in a Predator-Prey System with Generalized Group Defense and Impulsive Control Strategy

<table>Time series of system (<a href="https://static.hindawi.com/articles/ddns/volume-2013/358930/figures/#EEq1.4">11</a>) when <svg height="15.8375" id="M324" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 177.25 15.8375" width="177.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>; prey population <svg height="7.9499998" id="M325" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 9.625 7.9499998" width="9.625" 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="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
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</svg> and predator population <svg height="12.175" id="M326" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 9.9624996 12.175" width="9.9624996" 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="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
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</svg> coexist with periodic oscillations.</table>

Discrete Dynamics in Nature and Society

fig2

Figure 2

Figure 2: Complex Dynamical Behaviors in a Predator-Prey System with Generalized Group Defense and Impulsive Control Strategy 