Complex Dynamics of Discrete SEIS Models with Simple Demography

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="653937.fig.008a" src="https://static.hindawi.com/articles/ddns/volume-2011/653937/figures/653937.fig.008a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Forward-backward bifurcation</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="653937.fig.008b" src="https://static.hindawi.com/articles/ddns/volume-2011/653937/figures/653937.fig.008b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>A part of (a)</td></tr></table></td></tr></table>

<table>Forward-backward bifurcation for model (<a href="https://static.hindawi.com/articles/ddns/volume-2011/653937/figures/#EEq8">3.10</a>). The upper one occurs when <svg height="15.4" id="M465" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 44.987499 15.4" width="44.987499" 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="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117
t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z" id="x1D445"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.013,15.187)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
<g transform="matrix(.017,-0,0,-.017,22.062,11.112)"><path d="M512 230l-437 -233v58l378 199v2l-378 200v58l437 -233v-51z" id="x3E"></path></g><g transform="matrix(.017,-0,0,-.017,36.749,11.112)"><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>. Dotted lines represent unstable equilibria, and solid lines represent stable ones.</table>

Discrete Dynamics in Nature and Society

Complex Dynamics of Discrete SEIS Models with Simple Demography

Figure 8