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Chaos and nonlinear dynamics: an introduction for scientists and engineers, by Robert C. Hilborn, 2nd Ed., Oxford, Univ. Press, New York, 2004.
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in the range −1 to +1. This graph resembles a mouse.
181:{\displaystyle x_{n+1}=\exp(-\alpha x_{n}^{2})+\beta ,\,}
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248:can be chaotic. The map is also called the
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330:Bifurcation diagram of the Gauss map with
274:Bifurcation diagram of the Gauss map with
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98:), is a nonlinear iterated map of the
7:
1226:
1224:
564:Measure-preserving dynamical system
1244:. You can help Knowledge (XXG) by
102:into a real interval given by the
14:
1132:Oleksandr Mykolayovych Sharkovsky
376:in the range −1 to +1.
1228:
662:
654:
897:Rabinovich–Fabrikant equations
165:
141:
1:
349:{\displaystyle \alpha =6.20}
293:{\displaystyle \alpha =4.90}
221:In the parameter real space
71:{\displaystyle \beta =-0.58}
42:{\displaystyle \alpha =4.90}
632:Poincaré recurrence theorem
204:Johann Carl Friedrich Gauss
1312:
1223:
627:Poincaré–Bendixson theorem
979:Swinging Atwood's machine
652:
622:Krylov–Bogolyubov theorem
499:
78:. This shows an 8-cycle.
887:Lotka–Volterra equations
711:Synchronization of chaos
514:axiom A dynamical system
872:Double scroll attractor
637:Stable manifold theorem
544:False nearest neighbors
1240:-related article is a
912:Van der Pol oscillator
892:Mackey–Glass equations
524:Box-counting dimension
377:
370:
369:{\displaystyle \beta }
350:
321:
314:
313:{\displaystyle \beta }
294:
242:
199:are real parameters.
182:
79:
72:
43:
1062:Svetlana Jitomirskaya
969:Multiscroll attractor
814:Interval exchange map
767:Dyadic transformation
752:Complex quadratic map
594:Topological conjugacy
529:Correlation dimension
504:Anosov diffeomorphism
371:
351:
329:
315:
295:
273:
243:
241:{\displaystyle x_{n}}
183:
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23:of the Gauss map for
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1072:Edward Norton Lorenz
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334:
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278:
225:
113:
53:
27:
1032:Mitchell Feigenbaum
974:Population dynamics
959:Hénon–Heiles system
819:Irrational rotation
772:Dynamical billiards
757:Coupled map lattice
617:Liouville's theorem
549:Hausdorff dimension
534:Conservative system
519:Bifurcation diagram
254:bifurcation diagram
164:
1296:Chaos theory stubs
1210:Santa Fe Institute
1077:Aleksandr Lyapunov
907:Three-body problem
794:Gingerbreadman map
681:Bifurcation theory
559:Lyapunov stability
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68:
39:
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1218:
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1082:Benoît Mandelbrot
1047:Martin Gutzwiller
1037:Peter Grassberger
920:
919:
902:Rössler attractor
650:
649:
554:Invariant measure
476:Lyapunov exponent
382:
381:
104:Gaussian function
1303:
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1260:
1232:
1225:
1190:Butterfly effect
1102:Itamar Procaccia
1052:Brosl Hasslacher
949:Elastic pendulum
877:Duffing equation
824:Kaplan–Yorke map
742:Arnold's cat map
730:
706:Stability theory
691:Dynamical system
686:Control of chaos
666:
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642:Takens's theorem
574:Poincaré section
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1017:Mary Cartwright
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944:Double pendulum
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784:Exponential map
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90:(also known as
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1205:Predictability
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1200:Edge of chaos
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882:Lorenz system
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829:Langton's ant
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804:Horseshoe map
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701:Quantum chaos
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509:Arnold tongue
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1291:Chaotic maps
1246:expanding it
1238:chaos theory
1235:
1220:
1152:Mary Tsingou
1117:David Ruelle
1112:Otto Rössler
1057:Michel HĂ©non
1027:Leon O. Chua
984:Tilt-A-Whirl
954:FPUT problem
839:Standard map
834:Logistic map
788:
659:
433:Chaos theory
392:
262:
256:resembles a
252:because its
249:
220:
212:
208:logistic map
202:Named after
201:
196:
192:
190:
95:
92:Gaussian map
91:
87:
81:
1137:Nina Snaith
1127:Yakov Sinai
1012:Rufus Bowen
762:Duffing map
747:Baker's map
672:Theoretical
584:SRB measure
491:Phase space
461:Bifurcation
84:mathematics
21:Cobweb plot
1285:Categories
1195:Complexity
1092:Edward Ott
939:Convection
864:Continuous
539:Ergodicity
385:References
217:Properties
1107:Mary Rees
1067:Bryna Kra
1000:theorists
809:Ikeda map
799:HĂ©non map
789:Gauss map
471:Limit set
456:Attractor
364:β
338:α
308:β
282:α
250:mouse map
172:β
148:α
145:−
139:
96:mouse map
88:Gauss map
63:−
57:β
31:α
1183:articles
925:Physical
844:Tent map
734:Discrete
674:branches
604:Theorems
440:Concepts
1181:Related
989:Weather
927:systems
720:Chaotic
466:Fractal
1087:Hee Oh
722:maps (
569:Mixing
191:where
86:, the
1236:This
998:Chaos
777:outer
481:Orbit
258:mouse
100:reals
1242:stub
724:list
448:Core
356:and
344:6.20
300:and
288:4.90
195:and
66:0.58
49:and
37:4.90
136:exp
94:or
82:In
1287::
210:.
106::
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726:)
425:e
418:t
411:v
341:=
285:=
234:n
230:x
197:β
193:α
175:,
169:+
166:)
161:2
156:n
152:x
142:(
133:=
128:1
125:+
122:n
118:x
60:=
34:=
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