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Chaos of the new multiplicative logistic map
Shilong Gao1,2, Bixia Kan3
1College of Mathematics and Statistics, Leshan Normal University, Leshan, 614000, China. lunan1027@126.com.
Scientific Reports
|December 15, 2025
Summary
A new multiplicative logistic map offers enhanced chaotic dynamics and a wider output range than the classic version. This improved chaotic map shows promise for advanced encryption applications due to its flexibility and robustness.
Area of Science:
- Dynamical Systems and Chaos Theory
- Number Theory and Cryptography
Background:
- The classical logistic map is a foundational model in chaos theory.
- Limited dynamical range and parametric flexibility restrict its application in advanced cryptography.
Purpose of the Study:
- To introduce a novel multiplicative logistic map with extended dynamical capabilities.
- To analyze its chaotic behavior and assess its suitability for image encryption.
Main Methods:
- Derivation from multiplicative calculus principles.
- Theoretical analysis including stability and transversality conditions.
- Numerical simulations using bifurcation diagrams, cobweb, and time-series plots.
Main Results:
- The multiplicative logistic map exhibits a period-doubling bifurcation cascade into chaos.
- It demonstrates a broader chaotic region and an output range exceeding [0,1].
- Image encryption algorithms show strong resistance to statistical attacks and superior parameter robustness.
Conclusions:
- The proposed multiplicative logistic map possesses enhanced chaotic dynamics and flexibility.
- Its unique properties make it a strong candidate for secure image encryption.
- The extended range and robustness offer advantages over the classical logistic map in cryptographic applications.
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