Fast Consensus Seeking on Networks with Antagonistic Interactions

<div>(a) Original system <span class="nowrap"><svg height="9.25986pt" id="M626" style="vertical-align:-0.2455397pt" version="1.1" viewbox="-0.0498162 -9.01432 10.1863 9.25986" width="10.1863pt" 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="M417 653C377 677 335 687 290 687C171 687 83 622 83 541C83 462 150 415 250 398C231 363 224 320 224 292C224 212 282 165 361 165C409 165 455 180 499 209L500 208C439 89 369 16 246 16C183 16 127 48 122 79H124C131 68 141 66 153 66C181 66 197 90 197 117C197 142 173 164 146 164C111 164 87 134 87 95C87 39 157 -15 256 -15C421 -15 531 60 586 209C606 264 620 298 652 330L637 346C520 239 440 195 368 195C324 195 302 225 302 262C302 293 311 343 343 390C542 390 740 489 740 593C740 642 693 669 637 669C526 669 359 580 263 428C175 440 124 482 124 541C124 602 193 657 297 657C332 657 369 652 408 635L417 653ZM699 590C699 512 532 420 361 420C425 535 557 632 642 632C673 632 699 618 699 590Z"></path></g></svg>;</span> (b) the largest convergence rate system <span class="nowrap"><svg height="14.4885pt" id="M627" style="vertical-align:-5.474179pt" version="1.1" viewbox="-0.0498162 -9.01432 23.0702 14.4885" width="23.0702pt" 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="M417 653C377 677 335 687 290 687C171 687 83 622 83 541C83 462 150 415 250 398C231 363 224 320 224 292C224 212 282 165 361 165C409 165 455 180 499 209L500 208C439 89 369 16 246 16C183 16 127 48 122 79H124C131 68 141 66 153 66C181 66 197 90 197 117C197 142 173 164 146 164C111 164 87 134 87 95C87 39 157 -15 256 -15C421 -15 531 60 586 209C606 264 620 298 652 330L637 346C520 239 440 195 368 195C324 195 302 225 302 262C302 293 311 343 343 390C542 390 740 489 740 593C740 642 693 669 637 669C526 669 359 580 263 428C175 440 124 482 124 541C124 602 193 657 297 657C332 657 369 652 408 635L417 653ZM699 590C699 512 532 420 361 420C425 535 557 632 642 632C673 632 699 618 699 590Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.049,3.132)"><path d="M452 282C452 397 389 451 302 451C268 451 227 441 188 422C95 377 24 281 24 154C24 65 70 -12 173 -12C240 -12 297 16 342 52C418 113 452 201 452 282ZM359 282C359 163 308 66 247 39C237 35 225 32 212 32C151 32 114 79 114 157C114 301 180 380 223 398C240 405 250 408 265 408C315 408 359 369 359 282Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.796,3.132)"><path d="M573 302C573 402 527 451 414 451C386 451 343 446 313 437L330 513L320 522C295 508 261 484 243 463L230 415C194 400 159 383 126 359L131 330C159 344 187 357 222 368L109 -147C96 -204 80 -214 18 -223L13 -255L256 -244L259 -212L236 -210C184 -205 180 -195 191 -141L219 -1C240 -10 268 -12 284 -12C352 4 431 48 484 104C543 166 573 240 573 302ZM481 290C481 165 381 37 305 37C280 37 249 56 235 71L302 395C328 399 353 402 372 402C427 402 481 378 481 290Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,19.23,3.132)"><path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z"></path></g></svg>.</span></div>

Complexity

Fast Consensus Seeking on Networks with Antagonistic Interactions

Figure 3