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A unified framework for constructing two-dimensional bounded discrete systems
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DOI：doi:10.1088/1402-4896/adeed4.png)
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Abstract
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Creating kinetic amplitude-controlled two-dimensional (2D) hyperchaotic maps with robust hyperchaos is particularly important, but it is also very challenging. In this work, we present a unified framework for constructing 2D bounded discrete systems (2D-BDSs) with provable boundedness. To demonstrate its effectiveness, sixteen mapping models of 2D-BDSs are given by combining the mathematical relations of three bounded functions, sine, cosine, and hyperbolic tangent. Taking three specific mapping models of 2D-BDSs as examples, we use their fixed points with stability evolution to explore the bifurcation kinetics and coexistence behaviors under small-scale gains. Furthermore, taking four representative hyperchaotic maps from 2D-BDSs, we also explore the kinetic distributions under small-scale gains as well as the robust hyperchaotic behaviors and performance indexes under large-scale gains. The results show that the mapping models constructed by the unified 2D-BDS framework have the characteristics of controllable kinetic amplitudes, wide gain ranges, robust hyperchaos, and high-performance indexes. Additionally, a unified STM32 digital circuit is developed to demonstrate the implementation simplicity of the presented 2D-BDSs.
Keywords:
2D hyperchaotic maps
bounded discrete systems
kinetic amplitude control
robust hyperchaos
unified framework
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