Offset-Boosted Finite-Time Synchronization of a Multistable 3D Chaotic System with Circuit Validation and Analog Waveform Reconstruction Under AWGN

A piecewise-smooth three-dimensional chaotic system is presented in which multistability, controllable attractor translation, and synchronization-based analog waveform reconstruction are combined. Coexisting attractors are characterized through complementary local and global dynamical analyses, and offset boosting is used to translate the attractor without changing its intrinsic dynamics. Finite-time convergence is established analytically for the ideal controller under nominal matched conditions, whereas the smoothed controller used in the numerical study provides practical asymptotic synchronization. Analog realizability is examined through circuit simulation. The synchronized state is then used as a carrier for several representative bounded waveforms transmitted through an additive-noise channel. In the ideal channel, the reconstruction accuracy is determined directly by the remaining synchronization error. Under the investigated noisy-channel conditions, high fidelity is retained for the tested low-bandwidth waveforms, while greater distortion is observed for the broadband chirp because of the fixed receiver-filter bandwidth. The results therefore demonstrate the performance of the framework under the reported test conditions without implying universal noise robustness or cryptographic security.