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

## TL;DR

This paper introduces a new 3D chaotic system with adjustable offset and frequency control, suitable for secure communication and information transmission.

## Contribution

A novel chaotic system with flexible offset and frequency control is proposed, rare in existing research.

## Key findings

- The system can generate three distinct chaotic attractors and exhibits multidirectional offset boosting.
- Control constants effectively regulate the frequency of state variables and increase system complexity.
- DSP hardware experiments confirm the system's physical realizability and synchronization capabilities.

## Abstract

Signals with flexible control over polarity and frequency provide an essential foundation for reliable and high-speed information transmission. To generate chaotic signals with flexible output characteristics in low-dimensional systems, a novel chaotic system model is proposed by introducing a nonlinear term into the classical Chen chaotic system. Dynamical analysis and MATLAB numerical simulations show that the system is not only highly sensitive to initial conditions but also capable of generating three distinct chaotic attractors. Further simulations confirm that the proposed system demonstrates arbitrary unidirectional and multidirectional offset boosting behaviors, with offset amplitudes in all directions having a wide adjustable range. Furthermore, arbitrary offset constants can effectively control the frequencies of all state variables. This chaotic system, which combines flexible offset control with frequency regulation, is rare in existing research. Additionally, certain parameter ranges in the chaotic regime are relatively narrow. To address this, a method involving control constants to enhance system complexity is proposed, and its effectiveness in increasing system complexity is validated through Lyapunov spectrum and spectral entropy (SE) analysis. Based on the constructed chaotic system, an equivalent circuit model was built using the Multisim 14.0 platform. Experimental results confirm that the system generates chaotic attractors with distinct structures and demonstrates offset boosting behavior in arbitrary directions. Additionally, DSP hardware experiments further validate the physical realizability of the system. To fully exploit the system’s advantages, a synchronization controller was designed for both the drive and response systems, enabling synchronization control of the chaotic system with three offset constants. Based on this, data encryption and transmission experiments were conducted, further establishing the theoretical and experimental foundation for applying the new chaotic system in secure communication.