Abstract This study investigates the synchronous control of deoxyribonucleic acid (DNA) strand displacement loops in hyperchaotic conservative systems. It proposes an innovative solution to address limitations of traditional chaotic synchronisation techniques when handing high-dimensional systems, parameter uncertainties, and multi-system coordination. Differing from existing hyperchaotic conservative systems, this paper introduces a novel four-dimensional (4D) hyperchaotic conservative system. Through rigorous proofs of boundedness, dissipativity, and Hamiltonian energy conservation, the conservative nature of this system is established, revealing its unique dynamical behaviors, including nested conservative flows and offset boosting. To overcome the performance limitations of conventional synchronisation schemes, this study innovatively employs a loop controller composed of multiple strand displacement units, cascaded with the hyperchaotic conservative system, successfully achieving loop synchronisation of three 4D hyperchaotic conservative systems. This synchronisation strategy combines rapid convergence with robustness, featuring an adaptive compensation mechanism within the DNA strand displacement loop that effectively suppresses parameter perturbations, outperforming conventional control methods. Circuit simulations validate its physical feasibility, yielding a high-precision, interference-resistant signal source applicable to bio-computing and chaotic encryption, thereby demonstrating transformative application potential.
Yan et al. (Mon,) studied this question.
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