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Fractal Fract., Volume 10, Issue 6 (June 2026) – 2 articles

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28 pages, 42563 KB  
Article
Design of Multi-Cavity Chaotic Maps in the Polar Coordinate Using Nonlinear Curves and Modulo Operation with Application to Cavity-Based Data Hiding
by Bo Yan, Santo Banerjee and Shaobo He
Fractal Fract. 2026, 10(6), 351; https://doi.org/10.3390/fractalfract10060351 (registering DOI) - 22 May 2026
Abstract
At present, constructing discrete chaotic systems with unique characteristics and chaos has become a focal topic in the field of nonlinear research. This paper presents a new framework for designing multi-cavity chaotic maps in polar coordinates. It constructs the basic chaotic map through [...] Read more.
At present, constructing discrete chaotic systems with unique characteristics and chaos has become a focal topic in the field of nonlinear research. This paper presents a new framework for designing multi-cavity chaotic maps in polar coordinates. It constructs the basic chaotic map through nonlinear curves (such as Lotus curve, rose curves, and star curves) and generates multi-cavity attractors based on modular arithmetic. The nonlinear curves introduce complex deformations in the angular and radial components, while modular arithmetic serves as a folding mechanism to confine the dynamics to a specific range. The combined effect of these two elements forms multiple clearly separated chaotic cavities in the phase space. The number, size, shape, and chaotic characteristics of the cavities can be flexibly controlled by parameters. However, the introduction of fractional-order difference operators will disrupt the multi-chamber structure and make the system more complex. Furthermore, a data-hiding scheme based on the cavities is developed: the cavities act as natural isolation containers to embed information bits, and the chaotic dynamics provide encryption and confusion mechanisms. Experiments show that the designed chaotic map has high complexity and rich bifurcation behaviors; the data-hiding scheme performs well in terms of embedding capacity and security. Full article
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28 pages, 529 KB  
Article
Dissipativity and Stability for Stochastic Non-Integer-Order Memristive BAM System with Leakage Terms and Mixed Delays
by Weide Liu, Jiaxin Cheng and Hongfu Wang
Fractal Fract. 2026, 10(6), 350; https://doi.org/10.3390/fractalfract10060350 - 22 May 2026
Abstract
This paper is concerned with the problems of mean-square global dissipativity and global asymptotic stability for a class of stochastic fractional-order memristive BAM neural networks with leakage terms and mixed time-varying delays, including discrete delays and distributed delays. By using differential inclusion theory, [...] Read more.
This paper is concerned with the problems of mean-square global dissipativity and global asymptotic stability for a class of stochastic fractional-order memristive BAM neural networks with leakage terms and mixed time-varying delays, including discrete delays and distributed delays. By using differential inclusion theory, stochastic analysis, matrix measure approach, and Lyapunov stability theory combined with linear matrix inequalities (LMIs), several new sufficient conditions are derived to ensure the mean-square global dissipativity and global asymptotic stability of the considered system. Compared with the existing results, the obtained stability and dissipativity criteria are less conservative due to the adoption of matrix measure and fractional-order differential inequalities. The proposed model simultaneously incorporates stochastic perturbations, memristive discontinuity, leakage effects, and mixed delays, which makes it more consistent with actual engineering scenarios such as pattern recognition and intelligent control. Finally, a numerical example is provided to demonstrate the effectiveness and correctness of the theoretical results. Full article
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