Outer Synchronization of Simple Firefly Discrete Models in Coupled Networks

<div>Experimental fireflies synchronization: (a) isolated nodes, (b) line network synchronization with <svg height="8.80966pt" id="M243" style="vertical-align:-0.2129202pt" version="1.1" viewbox="-0.0498162 -8.59674 32.8954 8.80966" width="32.8954pt" 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="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="888" vert-adv-y="888"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.754,0)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.373,0)"><path d="M290 377C321 398 342 415 358 430C379 451 389 475 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C113 529 154 573 208 573C263 573 303 542 303 482C303 409 233 371 141 341L149 308C165 313 190 319 215 319C272 319 341 284 341 193C342 97 293 43 222 43C162 43 123 71 96 94C89 101 80 101 70 94C61 87 47 73 46 60C44 48 49 36 62 23S118 -12 165 -12C238 -12 430 62 430 223C430 298 379 359 290 375V377Z" id="g58-49"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>, (c) synchronization in three different networks with <svg height="8.80314pt" id="M244" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -8.59674 32.8954 8.80314" width="32.8954pt" 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="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="888" vert-adv-y="888"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.754,0)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.373,0)"><path d="M462 177V227H365V632H320C216 495 117 351 21 208V177H284V109C284 42 281 39 190 31V0H451V31C369 39 365 42 365 108V177H462ZM284 227H88C156 336 218 430 282 519H284V227Z" id="g58-50"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>, <svg height="8.80966pt" id="M245" style="vertical-align:-0.2129202pt" version="1.1" viewbox="-0.0498162 -8.59674 32.8954 8.80966" width="32.8954pt" 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="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="888" vert-adv-y="888"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.754,0)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.373,0)"><path d="M290 377C321 398 342 415 358 430C379 451 389 475 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C113 529 154 573 208 573C263 573 303 542 303 482C303 409 233 371 141 341L149 308C165 313 190 319 215 319C272 319 341 284 341 193C342 97 293 43 222 43C162 43 123 71 96 94C89 101 80 101 70 94C61 87 47 73 46 60C44 48 49 36 62 23S118 -12 165 -12C238 -12 430 62 430 223C430 298 379 359 290 375V377Z" id="g58-49"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>, and <svg height="8.80314pt" id="M246" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -8.59674 32.8954 8.80314" width="32.8954pt" 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="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="888" vert-adv-y="888"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.754,0)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.373,0)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 317 408 376 408 465C408 569 328 635 237 635C178 635 131 610 100 575L42 494L67 471C94 511 138 565 205 565C277 565 321 518 321 435C321 348 259 269 195 195C146 136 89 82 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g58-48"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>, and (d) network synchronization with <svg height="8.80966pt" id="M247" style="vertical-align:-0.2129202pt" version="1.1" viewbox="-0.0498162 -8.59674 32.8954 8.80966" width="32.8954pt" 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="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="888" vert-adv-y="888"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.754,0)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path><glyph.data ascent="3443" descent="-2856" 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Mathematical Problems in Engineering

fig24

Figure 24

Figure 24: Outer Synchronization of Simple Firefly Discrete Models in Coupled Networks 