Dual Projection Synchronization of Hyperchaotic Complex Systems with Complex Variables

Hyperchaotic complex systems are a type of dynamic system with complex variables. Compared with real-valued systems, the number of variables can be doubled, and they have the advantages of being more complex, higher-dimensional and more controllable. For such hyper-chaotic complex systems, a dual projective synchronization (DPS) scheme based on heterogeneous hyper-chaotic complex systems is proposed. First, a group of heterogeneous hyper-chaotic complex systems are selected, the real and imaginary parts of the state variables are separated, an equivalent system is obtained and analyzed by a mathematical model, and then the state variables are linearly coupled and used as a driving system; Then, combined with the idea of dual synchronization, a corresponding set of systems is selected, and its state variables are also linearly coupled as a response system. Lyapunov stability theory was used to design a DPS control scheme for heterogeneous hyperchaotic complex systems, and its rationality was proved mathematically. Finally, through numerical simulation, the efficiency and feasibility of the dual projection synchronization scheme were verified. It can provide new ideas and methods for the development of the field of chaos synchronization, and promote the application of chaotic systems in information transmission, encrypted communication and other fields.