ROUTE TO CHAOS IN THREE-DIMENSIONAL MAPS OF LOGISTIC TYPE.
1
Abstract : A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for
invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed
for ICC in the 2-dimensional case. When the parameter of the system is modified, localized oscillations occur on
the ICC that give rise to weakly chaotic rings, then to chaotic attractors, which finally disappear by contact
bifurcations. These maps can be considered as models for the symbiotic interaction of three species.
I INTRODUCTION
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II PERIOD DOUBLING OF INVARIANT CLOSED CURVES
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III FROM WEAKLY CHAOTIC RINGS TO CHAOS
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IV MULTISTABILITY
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V DISAPPEARANCE OF ATTRACTORS
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VI CONCLUSION
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REFERENCES
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