Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself?

<div>Stability surface of <svg height="11.5303pt" id="M209" style="vertical-align:-3.18148pt" version="1.1" viewbox="-0.0498162 -8.34882 37.9375 11.5303" width="37.9375pt" 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="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.525,0)"><path d="M474 0V26C414 34 401 43 364 100L267 248C300 297 324 332 345 358C381 400 394 405 455 411V437H272V411C316 406 323 401 305 370C287 337 267 306 247 276L188 369C169 397 173 405 215 411V437H16V411C71 404 83 396 114 348L201 212C171 167 144 127 116 92C77 42 66 34 4 26V0H190V26C139 34 136 43 156 77C175 113 198 150 220 183L294 66C311 39 302 31 260 26V0H474Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.661,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.239,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.502,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg> (in blue, the complex region where the point is an attractor, and in gray the surface where it is a repulsor or parabolic).</div>

Discrete Dynamics in Nature and Society

fig3

Figure 3

Figure 3: Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself? 