Analysis and Application of a 3D Chaotic System with Flexible Offset and Frequency Control

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Secure Communication Systems

Background:

• Flexible control over signal polarity and frequency is vital for reliable, high-speed information transmission.
• Existing low-dimensional chaotic systems often lack adaptable output characteristics.

Purpose of the Study:

• To propose a novel chaotic system model with flexible control over signal characteristics.
• To investigate the system's dynamical behaviors, including offset boosting and frequency regulation.
• To validate the system's physical realizability and explore its application in secure communication.

Main Methods:

• Introduction of a nonlinear term into the classical Chen chaotic system.
• Dynamical analysis and numerical simulations using MATLAB.
• Circuit modeling with Multisim 14.0 and experimental validation with DSP hardware.
• Design of a synchronization controller for chaotic systems.

Main Results:

• The proposed system exhibits high sensitivity to initial conditions and generates three distinct chaotic attractors.
• Demonstrates arbitrary unidirectional and multidirectional offset boosting with adjustable amplitudes.
• Achieves flexible frequency regulation of all state variables via offset constants.
• Validated physical realizability through circuit and DSP hardware experiments.
• Successful synchronization control and data encryption/transmission experiments.

Conclusions:

• The novel chaotic system offers rare combined features of flexible offset control and frequency regulation.
• The system is physically realizable and suitable for secure communication applications.
• The proposed model provides a strong theoretical and experimental basis for advanced chaotic signal applications.