Unpredictability of the Wada property in the parameter plane

2012 ◽  
Vol 376 (45) ◽  
pp. 3060-3066 ◽  
Author(s):  
Yongxiang Zhang ◽  
Guanwei Luo
Keyword(s):  
Parameter Plane ◽  
Wada Property

scholarly journals The game of Double-Silver on intervals

2001 ◽  
Vol 26 (8) ◽  
pp. 485-496 ◽  
Author(s):  
Gerald A. Heuer
Keyword(s):  
Measure Zero ◽  
Optimal Strategies ◽  
The Other ◽  
Parameter Plane ◽  
Left Endpoint ◽  
Relative Placement ◽  
Special Case

Silverman's game on intervals was analyzed in a special case by Evans, and later more extensively by Heuer and Leopold-Wildburger, who found that optimal strategies exist (and gave them) quite generally when the intervals have no endpoints in common. They exist in about half the parameter plane when the intervals have a left endpoint or a right endpoint, but not both, in common, and (as Evans had earlier found) exist only on a set of measure zero in this plane if the intervals are identical. The game of Double-Silver, where each player has its own threshold and penalty, is examined. There are several combinations of conditions on relative placement of the intervals, the thresholds and penalties under which optimal strategies exist and are found. The indications are that in the other cases no optimal strategies exist.

"CROSSROAD AREA–SPRING AREA" TRANSITION (II) FOLIATED PARAMETRIC REPRESENTATION

1991 ◽  
Vol 01 (02) ◽  
pp. 339-348 ◽  
Author(s):  
C. MIRA ◽  
J. P. CARCASSÈS ◽  
M. BOSCH ◽  
C. SIMÓ ◽  
J. C. TATJER
Keyword(s):  
Complete Information ◽  
Parametric Representation ◽  
Periodic Points ◽  
Parameter Plane ◽  
Flip Bifurcation ◽  
Cusp Point ◽  
Dimensional Representation ◽  
Bifurcation Structure ◽  
Spring Area

The areas considered are related to two different configurations of fold and flip bifurcation curves of maps, centred at a cusp point of a fold curve. This paper is a continuation of an earlier one devoted to parameter plane representation. Now the transition is studied in a thee-dimensional representation by introducing a norm associated with fixed or periodic points. This gives rise to complete information on the map bifurcation structure.

Numerical exploration of the parameter plane in a discrete predator–prey model

2015 ◽  
Vol 21 ◽  
pp. 112-119 ◽  
Author(s):  
P.P. Saratchandran ◽  
K.C. Ajithprasad ◽  
K.P. Harikrishnan
Keyword(s):  
Parameter Plane ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Numerical Exploration ◽  
Prey Model

scholarly journals A Study on the double crisis vertex in a twoparameter plane*

2002 ◽  
Vol 51 (12) ◽  
pp. 2694
Author(s):  
Hong Ling ◽  
Xu Jian-Xue
Keyword(s):  
Parameter Plane ◽  
Two Parameter

THE OSCILLATION–ROTATION ATTRACTORS IN THE FORCED PENDULUM AND THEIR PECULIAR PROPERTIES

2002 ◽  
Vol 12 (01) ◽  
pp. 159-168 ◽  
Author(s):  
WANDA SZEMPLIŃSKA-STUPNICKA ◽  
ELŻBIETA TYRKIEL
Keyword(s):  
Control Parameter ◽  
Fractal Structure ◽  
Basins Of Attraction ◽  
Parameter Plane ◽  
System Control ◽  
Periodic Force ◽  
Forced Pendulum ◽  
Insight Into

The paper is aimed at exploration of the properties of the oscillation–rotation attractors in the dissipative pendulum driven by external periodic force. The study of regions of existence of the orbits in the system control parameter plane, coexistence with other attractors, fractal structure of their basins of attraction, and the role they play in the onset of the tumbling chaos, give an insight into some peculiar features of the oscillation–rotation attractors and their bifurcational structures.

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