Synchronization Simulation of Complex Nonlinear Coupled Networks

This project conducts synchronization simulation for a complex nonlinear coupled network with 50 nodes. To simulate networks with more nodes, simply modify the scalar dimension parameters in the module configuration, typically by adjusting the array size variables in the initialization script. For a more detailed description of this process, let's first explain what a complex nonlinear coupled network is. A complex nonlinear coupled network consists of multiple nodes where each node possesses its own state variables and coupling mechanisms. By adjusting the coupling strength and coupling methods between nodes, network synchronization can be achieved. In this simulation, we use Lorenz chaotic nodes as network elements and define inter-node coupling relationships through the generation of a K matrix. The generation of the K matrix is a crucial step that determines both the coupling strength and coupling topology between nodes. This is typically implemented through weighted adjacency matrix construction using mathematical operations like matrix multiplication and eigenvalue decomposition. By adjusting the numerical values in the K matrix, we can control the network synchronization effect. While this simulation uses a 50-node network, you can easily scale it to more nodes by modifying the dimension parameters in the module configuration files. Once the K matrix is generated, we run the simulation using Simulink. Simulink is a widely-used simulation tool that helps model and visualize network synchronization curves through block diagram programming. The simulation employs differential equation solvers and state-space modeling to compute node dynamics. Through simulation, we can observe synchronization effects between nodes and obtain synchronization curves that demonstrate convergence behavior. In summary, by conducting synchronization simulation on a 50-node complex nonlinear coupled network, we obtain synchronization curves for a complex network of 50 Lorenz chaotic nodes. This process involves two key steps: generating the K matrix (implemented through adjacency matrix algorithms) and running Simulink simulations (using ODE solvers and state-space models). By adjusting coupling strength and coupling methods through matrix parameter modification, we can effectively control the network synchronization performance.