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A Cascading Framework for Integrating Chaotic Maps and Generating Complex Dynamics
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DOI：10.1109/ACCESS.2026.3705975.png)
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Abstract
En 中文
This work proposes a generalized cascading framework to integrate low-dimensional chaotic maps through a nonlinear transformation layer comprising transcendental equations. The framework is map-agnostic and introduces composition of two heterogeneous maps without altering the internal structural dynamics of the component maps. Theoretical analysis also establishes local invertibility and perturbation propagation through Jacobian-based analysis. A representative instantiation integrating classical 2D Logistic and 2D Ikeda maps is presented to validate the dynamical enhancement through bifurcation analysis, Lyapunov exponent estimation and attractor analysis. Results reveal that the resultant system achieves increased dynamical richness compared to the individual component maps. As an application, a chaos-based pseudorandom number generator is also designed to demonstrate the practical applicability of the framework. Extensive statistical evaluation and empirical security assessment, supported by chaos-oriented test data-generation mechanisms, is conducted to analyze seed perturbation, avalanche behavior and seed entropy degradation characteristics. The proposed framework provides a practical and resource-efficient pathway for achieving enhanced dynamical complexity through controlled interactions among low-dimensional component maps while maintaining structural modularity and heterogeneity.
Keywords:
Cascading framework
chaos-based PRNG
chaotic maps
Jacobian matrix
Lyapunov exponent
Journal
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3.6
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9.8W
Citations:
29.4W