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The q-deformed Tinkerbell map
Sudharsana V Iyengar1, Janaki Balakrishnan1
1School of Natural Sciences and Engineering, National Institute of Advanced Studies, Indian Institute of Science Campus, Bangalore 560 012, India.
Chaos (Woodbury, N.Y.)
|December 4, 2018
Summary
Q-deformed Tinkerbell maps exhibit complex dynamics, including multiple co-existing attractors. This study demonstrates their potential for secure data encryption and decryption using initial conditions and deformation parameters.
Area of Science:
- * Dynamical systems
- * Chaos theory
- * Mathematical physics
Background:
- * Q-deformations are mathematical tools used to explain experimental phenomena.
- * The Tinkerbell map is a discrete dynamical system known for its complex behavior.
Purpose of the Study:
- * To investigate the dynamical behavior of the Tinkerbell map under q-deformations.
- * To explore the potential of q-deformed Tinkerbell maps for secure communication.
Main Methods:
- * Numerical analysis of the Tinkerbell map with varying q-deformation parameters.
- * Investigation of bifurcations, attractors, and multistability.
- * Application of the system's sensitivity for cryptographic purposes.
Main Results:
- * Rich dynamical behaviors observed, including interior crises and cascades.
- * Simultaneous occurrence of Neimark-Sacker and reverse Neimark-Sacker bifurcations.
- * Existence of 3 co-existing limit cycles in specific parameter ranges.
- * Demonstrated secure encryption and decryption of messages.
Conclusions:
- * Q-deformed Tinkerbell maps display complex dynamics and multistability.
- * The system's sensitivity allows for secure data transmission.
- * Proposed as a novel method for secure message encryption and decryption.
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