Chaos Synchronization of the Lu System Using Single-Variable Feedback

This paper explores a simple yet effective way to synchronize the chaotic Lü system using just one variable from the master system. Rather than relying on full-state observation or advanced nonlinear control, the method uses a straightforward linear feedback approach and takes advantage of the inherent stability in cascade-connected systems to achieve synchronization. One of the main strengths of this approach is its efficiency. By transmitting only a single state variable, it keeps communication demands low—something that’s especially helpful in real-time applications or when resources are limited. Another benefit is that the method doesn’t depend on knowing the bounds of the master system’s trajectories in advance, which makes it more flexible for systems that are unpredictable or constantly changing. The controller itself is also relatively simple to put into practice, avoiding the complexity often seen in other synchronization methods. The approach is backed by solid theoretical analysis, and simulation results using MATLAB show that it works well in practice. Overall, this method offers a lightweight and practical solution for chaos synchronization—ideal for situations where minimal data and easy implementation are key.