Delayed q-deformed logistic map

•The interplay between complexity brought by q-deformation and order by delay is studied in logistic map.•Delay suppresses chaos for Tsallis and Qu-group type of deformations with stabilization of period-1 and -2, respectively.•Increasing delay maintains steady state in Tsallis type while chaotic st...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2013-11, Vol.18 (11), p.3126-3133
Main Authors: Shrimali, Manish Dev, Banerjee, Subhashish
Format: Article
Language:English
Subjects:
Chaos theory
Computer simulation
Deformation
Delay
Logistic map
Logistics
Mathematical analysis
Mathematical models
Q-deformation
Steady state
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Summary:•The interplay between complexity brought by q-deformation and order by delay is studied in logistic map.•Delay suppresses chaos for Tsallis and Qu-group type of deformations with stabilization of period-1 and -2, respectively.•Increasing delay maintains steady state in Tsallis type while chaotic state is recovered in Qu-group type of deformation. The delay logistic map with two types of q-deformations: Tsallis and Quantum-group type are studied. The stability of the logistic map and its bifurcation scheme is analyzed as a function of the deformation and delay parameters. Chaos is suppressed in a certain region of deformation and delay parameter space. By introducing delay, the steady state in one type of deformation is maintained while chaotic behavior is recovered in another type.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2013.03.017