Publication Details:
Journal or Publication Title:
Armenian Journal of Physics=Ֆիզիկայի հայկական հանդես
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Title:
One-dimensional Dynamics for a Discontinuous Singular Mapand the Routes to Chaos
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Department of Physics and Physical Oceanography University of North Carolina Wilmington
Subject:
Uncontrolled Keywords:
logistic map ; fixed points ; stability ; transition to chaos ; Sarkovskii’s theorem ; aperiodicity
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Abstract:
We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points x0. In particular, routes to chaos exist that do not exhibit period-doubling whereas period-doubling is the sole route to chaos in the logistic map. Aperiodic maps are found that lead to cobwebs with x = ±∞ as accumulation points, where every neighborhood contains infinitely many points generated by the map.