Increased-Order Generalized Synchronization in Memristive Neurons: Analytical and Data-Driven Approaches
Abstract
We investigate increased-order generalized synchronization between four- and five-dimensional memristive Hindmarsh--Rose neurons, focusing on the selection and stabilization of the synchronization map. An analytical construction combines a prescribed nonlinear map with adaptive control, retaining the memristive switching contribution explicitly in the error dynamics. Lyapunov analysis establishes asymptotic synchronization under uniform strict dissipativity and yields a switching-independent decrease estimate outside an explicit error neighborhood. Numerical simulations exhibit error decay beyond the sufficient convergence conditions. A complementary data-driven construction uses next-generation reservoir computing to learn predictors from uncoupled full-state trajectories and an affine synchronization map through dynamical consistency. The resulting sampled-data controller achieves small residual tracking errors without access to the governing equations. Relative to a reference map within the data-driven framework, the learned map reduces median control effort approximately eightfold while improving tracking accuracy. These results connect synchronization-map selection with conditional convergence guarantees and reduced control requirements.
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BibTeX
@misc{mustafic2026increasedorder,
title = {{Increased-Order Generalized Synchronization in Memristive Neurons: Analytical and Data-Driven Approaches}},
author = {Dennis Mustafić and Marius E. Yamakou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25164},
eprint = {2610.25164},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25164},
}
RIS
TY - UNPB
TI - Increased-Order Generalized Synchronization in Memristive Neurons: Analytical and Data-Driven Approaches
AU - Dennis Mustafić
AU - Marius E. Yamakou
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25164
UR - https://arxiv.org/abs/2610.25164
AB - We investigate increased-order generalized synchronization between four- and five-dimensional memristive Hindmarsh--Rose neurons, focusing on the selection and stabilization of the synchronization map. An analytical construction combines a prescribed nonlinear map with adaptive control, retaining the memristive switching contribution explicitly in the error dynamics. Lyapunov analysis establishes asymptotic synchronization under uniform strict dissipativity and yields a switching-independent decrease estimate outside an explicit error neighborhood. Numerical simulations exhibit error decay beyond the sufficient convergence conditions. A complementary data-driven construction uses next-generation reservoir computing to learn predictors from uncoupled full-state trajectories and an affine synchronization map through dynamical consistency. The resulting sampled-data controller achieves small residual tracking errors without access to the governing equations. Relative to a reference map within the data-driven framework, the learned map reduces median control effort approximately eightfold while improving tracking accuracy. These results connect synchronization-map selection with conditional convergence guarantees and reduced control requirements.
ER -