Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2103.02880

Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators

Yuzuru Kato·Anatoly Zlotnik·Jr-Shin Li·Hiroya Nakao
View original source ↗Read source document ↗Export metadata ↓

Abstract

We propose a general method for optimizing periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators based on phase reduction and nonlinear programming. We derive averaged phase dynamics from the mathematical model of a limit-cycle oscillator driven by a weak periodic input and optimize the Fourier coefficients of the input waveform to maximize prescribed objective functions. In contrast to the optimization methods that rely on the calculus of variations, the proposed method can be applied to a wider class of optimization problems including global entrainment objectives. As an illustration, we consider two optimization problems, one for achieving fast global convergence of the oscillator to the entrained state and the other for realizing prescribed global phase distributions in a population of identical uncoupled noisy oscillators. We show that the proposed method can successfully yield optimal input waveforms to realize the desired states in both cases.

Explore related subjects

nlin.AO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yuzuru Kato, Anatoly Zlotnik, Jr-Shin Li, Hiroya Nakao. 2021-07-27. Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators. https://doi.org/10.1007/s11071-021-06703-w

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

KEEP EXPLORING

Related papers

arXiv2026

Self-Organization to the Edge of Ergodicity Breaking in a Complex Adaptive System

Self-organized criticality is widely invoked for collective behavior, yet its role in objective-driven, heterogeneous adaptive systems is unclear. We introduce {\tt EvoSK}: agents learn on a Sherrington--Kirkpatrick landscape while the least fit are replaced. It self-organizes to the edge of ergodicity breaking, with scale-free avalanches ($τ\approx -1.5$) and rewards beating any tuned non-evolutionary regime. Its cascade's branching ratio is the spectral radius of the learning dynamics' Jacobian, making critical branching and ergodicity breaking one marginal-stability condition fixing the exponent. The attraction to criticality follows from the selection--mutation balance: subcritical cascades decay too fast to dislodge frozen agents, supercritical cascades shield them from selection; only the critical power-law tail supplies the polynomial rate the balance requires.

nlin.AO↗
arXiv2026

When higher-order interactions enhance synchronization: the case of the Kuramoto model

Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled oscillators, traditionally assuming pairwise interactions. However, many real-world systems exhibit group and many-body interactions, which can be effectively modeled through hypergraphs. Here we show that the effect of such higher-order interactions on synchronization is non-monotonic. Through a numerical study of higher-order Kuramoto models on random hypergraphs and on globally coupled systems, we find that the degree of synchronization reached from incoherent initial conditions is maximized at a small but nonzero higher-order coupling strength: weak higher-order interactions enhance synchronization when added to pairwise ones, whereas strong ones work against it, in line with earlier reports of reduced basins and of cluster states. We further show, through a cost-constrained allocation analysis, that under a constrained budget for interactions a mixed allocation of pairwise and higher-order couplings consistently achieves higher synchronization than relying on either type alone. These findings clarify the role of higher-order interactions in shaping collective dynamics and point to design principles for optimizing synchronization in complex systems.

nlin.AO↗
arXiv2026

Dynamics-preserving network reductions for ride-pooling paths

Reducing the complexity of ride-pooling paths is a central challenge in systems with distributed demand. Here we show that such dynamics admit an exact coarse-grained representation: for a broad class of routing algorithms whose decisions depend only on path lengths, the full network can be reduced to an effective network of active nodes weighted by shortest-path distances without altering the resulting trajectories, up to stochastic degeneracy breaking. The reduction therefore defines an equivalence class of network representations generating identical path dynamics. We further demonstrate that for globally optimizing dispatchers this equivalence is systematically violated through degeneracy amplification, yet remains quantitatively accurate beyond the exactly solvable regime. Our results identify when spatial structure can be integrated out without loss of dynamical fidelity, providing a general framework for the analysis of interacting path processes.

nlin.AO↗