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Design and implementation of a heterogeneous multi-cavity hyperchaotic map derived from complex exponential

Zeping Zhang1, Huihai Wang1, Kehui Sun2

  • 1School of Electronic Information, Central South University, Changsha 410083, China.

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A novel complex exponential chaotic map (CECM) and heterogeneous multi-cavity hyperchaotic map (HMCM) were developed to increase structural complexity. Dynamical analyses and hardware implementation confirm robust hyperchaotic performance and low resource usage.

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Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Science
  • Chaos Theory

Background:

  • Enhancing structural complexity in multi-cavity chaotic maps is crucial for advanced applications.
  • Existing chaotic maps often lack sufficient complexity for sophisticated systems.

Purpose of the Study:

  • To introduce a new complex exponential chaotic map (CECM) for increased structural complexity.
  • To develop a heterogeneous multi-cavity hyperchaotic map (HMCM) by integrating CECM with step functions.
  • To verify the hyperchaotic performance and hardware feasibility of the proposed map.

Main Methods:

  • Development of a novel complex exponential chaotic map (CECM).
  • Integration of CECM with step functions to create a heterogeneous multi-cavity hyperchaotic map (HMCM).
  • Dynamical analyses including phase diagrams, Lyapunov exponents, and permutation entropy.
  • Implementation on a digital signal processor (DSP) for on-chip analysis.

Main Results:

  • The CECM exhibits parameter-sensitive attractor shapes.
  • The HMCM generates multiple cavities with unique structures, significantly enhancing system complexity.
  • Dynamical analyses confirm robust hyperchaotic behavior across a wide parameter range.
  • Hardware implementation on DSP validates physical feasibility, stable chaos, and low resource requirements.

Conclusions:

  • The proposed HMCM offers enhanced structural complexity and robust hyperchaotic performance.
  • The map is suitable for hardware implementation due to its low-resource usage and physical feasibility.
  • This work contributes a novel approach to designing complex chaotic systems for potential applications.