Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.25164

Increased-Order Generalized Synchronization in Memristive Neurons: Analytical and Data-Driven Approaches

Dennis Mustafić·Marius E. Yamakou
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

nlin.AOmath.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dennis Mustafić, Marius E. Yamakou. 2026-10-18. Increased-Order Generalized Synchronization in Memristive Neurons: Analytical and Data-Driven Approaches. https://arxiv.org/abs/2610.25164

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Multifractality of human upper-limb velocity tracks motor optimization via hand dominance experiment

Theoretical goal-directed movements follow a unique, stereotyped velocity profile, but continuous movement has no unique optimal solution, so it is unclear whether motor optimization makes continuous movement more stereotyped or more diverse. Previous studies indicated higher information content in the dominant hand, suggesting greater diversity. Because continuous velocity is a composition of overlapping joints movement of varying form, timing and amplitude, comparable to the events that compose spike trains and heartbeat series, we asked whether this diversity appears as a wider multifractal spectrum of velocity. We applied multifractal detrended fluctuation analysis to motion-capture velocity of cursive handwriting from right- and left-handed participants writing with both hands; hand dominance is a natural experiment in which task and geometry are fixed while optimization varies. With the dominant hand, spectra were wider, had a lower dominant exponent and were more positively asymmetric in both groups, whereas hands with the same functional role did not differ between groups. A logistic regression on the three spectral features identified the dominant hand with a cross-validated AUC of up to 0.93. Optimized continuous movement is thus not more stereotyped but more diverse: complex, neither stereotyped nor random, with multifractality that tracks hand dominance.

nlin.AO↗
arXiv2026

Linear Approximations Provide Rigorous Conditions for Phase Locking in Oscillator Networks and Power Grids

Synchronization is a fundamental collective phenomenon in many natural and engineered networks. The stable operation of oscillator networks, such as electric power grids, requires phase locking with phase differences across edges below a given threshold. A central question is whether a given network supports such a state. In this contribution, we extend a convex optimization formulation of the nonlinear fixed point equations of the Kuramoto model, that also describe lossless power grids. Based on this formulation, we derive rigorous and tight bounds on the error introduced by an arbitrary approximation of the original model, in particular linear approximations. The bounds yield edge-wise regions of trust around the approximation, within which the true nonlinear solution must lie. They further provide sufficient and necessary conditions for phase locking under prescribed phase difference limits. Numerical experiments show that the bounds are tight over a broad range of parameters.

nlin.AO↗
arXiv2026

Noise-induced transitions between coexisting limit cycles beyond saddle-node bifurcations

Nonlinear multistable systems with limit cycles may exhibit noise-induced transitions between oscillatory states, even in parameter regimes beyond the saddle-node bifurcations that determine the existence of these limit cycles. This behavior is associated with the ghost of a saddle-node bifurcation, a well-known feature of nonlinear systems near such bifurcation points. To investigate this phenomenon, we first consider a stochastic minimal model that supports two coexisting limit cycles within a parameter interval bounded by two saddle-node bifurcations. We numerically and theoretically estimate the probability of remaining near each stable attractor as a function of both the noise intensity and the distance to the ghost structure. The model is then extended by introducing spatially localized, non-homogeneous noise with enhanced intensity in a prescribed region of phase space. This modification is intended to emulate the asymmetric structure of the Hindmarsh-Rose model, in which bursting limit cycles approach each other closely in specific regions of phase space, thereby facilitating noise-induced transitions between them.

nlin.AO↗