Eigenvalue Spectrum and Synchronizability of Two Types of Double-Layer Star-Ring Networks with Hybrid Directional Coupling

<div>When <i>N</i> is even, the synchronizability of Network II changes with the interlayer coupling strength <i>d</i> between the leaf nodes. (a) <svg height="12.4698pt" id="M427" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 12.8362 12.4698" width="12.8362pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><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></svg> changes with <i>d</i> (<i>d</i> changes from 0.01 to 1); (b) <i>R</i> changes with <i>d</i> (<i>d</i> changes from 0.01 to 1).</div>

Discrete Dynamics in Nature and Society

fig17

Figure 17

Figure 17: Eigenvalue Spectrum and Synchronizability of Two Types of Double-Layer Star-Ring Networks with Hybrid Directional Coupling 