Stability, Bifurcation, and Chaos Control of Two-Sided Market Competition

<div>Bifurcation diagram with respect to <svg height="9.3838pt" id="M164" style="vertical-align:-0.07589912pt" version="1.1" viewbox="-0.0498162 -9.3079 6.57182 9.3838" width="6.57182pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M513 0V26C475 28 448 43 413 81C379 116 277 234 258 264C301 314 319 334 344 359C383 396 404 407 473 418V443L269 434V408C317 403 320 395 299 364C280 337 250 298 228 276C213 260 195 247 165 241V712C126 699 69 682 21 677V653C82 648 87 642 87 576V104C87 40 81 32 14 26V0H237V26C173 32 165 38 165 104V215C171 217 176 218 181 218C189 218 198 212 212 196C267 129 330 49 376 -2L513 0Z"></path></g></svg> and the maximum Lyapunov exponent with respect to k when <span class="nowrap"><svg height="12.7373pt" id="M165" style="vertical-align:-3.429399pt" version="1.1" viewbox="-0.0498162 -9.3079 199.491 12.7373" width="199.491pt" xmlns="http://www.w3.org/2000/svg" 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International Journal of Computer Games Technology

fig13

Figure 13

Figure 13: Stability, Bifurcation, and Chaos Control of Two-Sided Market Competition 