Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function

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397Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.173,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.751,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.014,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.254,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.218,0)"><path 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(b) The enlargement corresponds to the red box in Figure <a href="../fig3/#a">3(a)</a>, while we increase the number of periods to 200 and abundant dynamic phenomena appear. (c) The enlargement corresponding to the white box in Figure <a href="../fig3/#b">3(b)</a>, where we can clearly see that ISSs (shrimp-like) structures exist, which are labeled by <b>a</b>, <b>b</b>, and <b>c</b> (d). The 2D Lyapunov exponent diagram corresponding to Figure <a href="../fig3/#b">3(b)</a>.</div>

Complexity

fig3

Figure 3

Figure 3: Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function 