Dislocated Projective Synchronization of Parameter-Perturbed Hyperchaotic Systems Based on DNA Strand Displacement and Its Secure Communication

Abstract

DNA strand displacement (DSD) has enabled significant advances in chaotic secure communication. However, DSD-based drive–response systems often suffer from limited complexity and rigid dynamic control, reducing their adaptability under complex biochemical conditions. To address these limitations, this paper proposes a Dislocated Perturbation Secure Communication (DPSC) scheme based on DSD mechanisms. First, a hyperchaotic system is designed according to the dual-rail representation and law of mass action, integrating emergence, catalysis, fasciation, and annihilation modules. The Chen hyperchaotic system is employed as a parameter perturbation source, and an active perturbation strategy is introduced to emulate nonlinear biochemical fluctuations. Subsequently, a DSD-based Dislocated Perturbation Controller (DPC) is constructed to achieve dislocated projective synchronization, ensuring system stability and accurate dynamic mapping between the drive and response states. Finally, the perturbation-driven hyperchaotic signal is utilized for secondary encryption of the drive signal, significantly enhancing communication security. Numerical simulations confirm that the DPSC-encrypted signal exhibits enhanced complexity and improved resilience to external disturbances as compared to traditional chaotic masking techniques. Furthermore, the receiver is capable of reconstructing the initial signal with high fidelity and without distortion.