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Related Experiment Video

Updated: Jun 7, 2025

Assembly and Characterization of Biomolecular Memristors Consisting of Ion Channel-doped Lipid Membranes

Assembly and Characterization of Biomolecular Memristors Consisting of Ion Channel-doped Lipid Membranes

Published on: March 9, 2019

A novel discrete memristive hyperchaotic map with multi-layer differentiation, multi-amplitude modulation, and

Xinyan Wang¹, Yuqi Wei¹, Xu Sun¹

¹School of Electronic Engineering, Heilongjiang University, Harbin 150080, China.

Chaos (Woodbury, N.Y.)

|November 20, 2024

Summary

A new three-dimensional discrete memristive hyperchaotic map (3D-DMCHM) enhances chaotic map complexity and controllability. This memristor-based system shows promising applications in secure communication and random number generation.

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Area of Science:

Nonlinear Dynamics and Chaos Theory
Memristor Applications
Secure Communication Systems

Background:

Memristors enhance chaotic maps, improving complexity and controllability.
Chaotic maps are crucial for secure communication and random number generation.
Discrete chaotic maps with memristors offer advanced functionalities.

Purpose of the Study:

To construct and analyze a novel three-dimensional discrete memristive hyperchaotic map (3D-DMCHM).
To investigate the complex dynamical behaviors and unique phenomena of the 3D-DMCHM.
To confirm the map's complexity and hardware feasibility for practical applications.

Main Methods:

Construction of a 3D-DMCHM using a cosine memristor.
Analysis of fixed points, stability, phase diagrams, bifurcation diagrams, and Lyapunov exponents.
Investigation of attractor basins, timing diagrams, and complexity tests.

Main Results:

The 3D-DMCHM exhibits complex dynamics, entering chaos via period-doubling bifurcation.
Observed phenomena include multi-layer differentiation, multi-amplitude control, and offset boosting.
Unique offset behaviors with hidden chaotic attractors or coexisting attractors were identified.
Complexity tests and digital signal processing circuit implementation confirmed high complexity and hardware feasibility.

Conclusions:

The developed 3D-DMCHM demonstrates significant complexity and controllability.
The map exhibits unique dynamical behaviors and phenomena.
The hardware implementation confirms the practical feasibility of the 3D-DMCHM for secure communication and random number generation.