MATLAB Implementation of Chua's Chaotic Synchronization

Chua's chaotic synchronization is a classical method for synchronizing chaotic systems, commonly used in nonlinear dynamical system research. Its core mechanism involves achieving state synchronization between two chaotic systems through a drive-response configuration.

When implementing Chua's chaotic synchronization in MATLAB, it typically requires constructing master-slave system models. Both the master system (drive system) and slave system (response system) are described using the nonlinear equations of Chua's circuit. By designing appropriate control laws, the slave system's state variables can track the master system, thereby achieving synchronization.

The program implementation mainly consists of the following components: Chua's System Modeling: Define differential equations for master and slave systems, typically containing nonlinear terms (such as piecewise linear functions). Key implementation involves declaring state variables (x,y,z) and parameters (α,β) using function handles or separate m-files. Synchronization Controller Design: Design control signals based on error dynamics, commonly using methods like linear feedback control or adaptive control. Algorithm implementation requires calculating state differences and applying control gains to minimize synchronization errors. Numerical Solving: Simulate system evolution using MATLAB's ODE solvers (e.g., `ode45`). Critical configuration includes setting time span, initial conditions, and parameter tuning through odeset options. Result Visualization: Plot state trajectories of master-slave systems and synchronization error curves to validate synchronization performance. Implementation typically uses subplot arrangements with plot3 for 3D trajectories and error analysis through time-domain plots.

Chua's chaotic synchronization finds wide applications in secure communication and signal encryption domains. By adjusting system parameters and control gains, researchers can investigate synchronization performance under different conditions through parameter sweep simulations.