Time-Delay Characteristics of Complex Lü System and Its Application in Speech Communication

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Secure Communications

Background:

• Complex Lü systems are widely studied for their chaotic behavior.
• The application of self-time-delay synchronization (STDS) in complex Lü systems for secure speech communication is underexplored.
• Existing literature lacks comprehensive studies on STDS for complex Lü systems in practical communication scenarios.

Purpose of the Study:

• To investigate the self-time-delay synchronization (STDS) of a complex Lü system with double time-delay.
• To design an effective synchronization controller for achieving STDS in these systems.
• To develop and evaluate a secure speech communication scheme utilizing the STDS of complex Lü systems.

Main Methods:

• Introduction and analysis of a complex Lü system featuring double time-delay.
• Design of a synchronization controller to achieve STDS.
• Development of a speech communication scheme based on the improved STDS controller.
• Validation of the controller and communication scheme through numerical simulations.

Main Results:

• The chaotic characteristics of the double time-delay complex Lü system were analyzed.
• A novel synchronization controller was successfully designed to achieve STDS.
• The proposed STDS controller enabled the development of an effective secure speech communication scheme.
• Simulation results confirmed the effectiveness of both the controller and the communication system.

Conclusions:

• The study successfully demonstrated the feasibility of STDS for complex Lü systems with double time-delay.
• A new synchronization controller and a secure speech communication scheme were developed and validated.
• This research contributes a novel approach to secure communication using chaotic systems, addressing a gap in the literature.