Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities

<div>Chaos attractors for (a) <span class="nowrap"><svg height="12.4698pt" id="M71" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 116.083 12.4698" width="116.083pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z" id="g113-223"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.557,3.132)"><path d="M389 0V32C297 38 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Discrete Dynamics in Nature and Society

fig8

Figure 8

Figure 8: Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities 