A sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systems

Abstract We study identical semi-passive systems coupled pairwise by heterogeneous, linear or nonlinear passive systems, including systems with memory such as memristive systems. The semi-passive systems are assumed to satisfy a certain input–output symmetry and can for instance be oscillators with...

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Main Authors: Robin Lautenbacher, Jonas Röhrig, Karlheinz Ochs, Ralf Köhl
Format: Article
Language:English
Published: Springer 2025-06-01
Series:Discover Applied Sciences
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Online Access:https://doi.org/10.1007/s42452-025-07140-9
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author Robin Lautenbacher
Jonas Röhrig
Karlheinz Ochs
Ralf Köhl
author_facet Robin Lautenbacher
Jonas Röhrig
Karlheinz Ochs
Ralf Köhl
author_sort Robin Lautenbacher
collection DOAJ
description Abstract We study identical semi-passive systems coupled pairwise by heterogeneous, linear or nonlinear passive systems, including systems with memory such as memristive systems. The semi-passive systems are assumed to satisfy a certain input–output symmetry and can for instance be oscillators with an asymptotically stable limit cycle or systems with asymptotically stable equilibrium, but also chaotic systems or neuronal oscillators. We represent the system of coupled semi-passive systems by a graph. The semi-passive systems are associated with the nodes of that graph and the nonlinear passive systems are associated with the graphs edges. To each such system we associate a weight defined as the largest value w.r.t. which the system is input- or output-passive. We derive a sufficient condition for synchronization that is phrased in terms of the algebraic connectivity of the weighted coupling graph, a generalized one-sided Lipschitz-condition associated to the semi-passive system and a constant related to its linear input–output-behavior. We also derive a sufficient condition for output synchronization in a border-line case where our main condition is not applicable.
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spelling doaj-art-9c1abd9da46d4038956c00a55282cb322025-08-20T03:45:32ZengSpringerDiscover Applied Sciences3004-92612025-06-017612410.1007/s42452-025-07140-9A sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systemsRobin Lautenbacher0Jonas Röhrig1Karlheinz Ochs2Ralf Köhl3Mathematics Seminar, Kiel UniversityChair of Digital Communication Systems, Ruhr-University BochumChair of Digital Communication Systems, Ruhr-University BochumMathematics Seminar, Kiel UniversityAbstract We study identical semi-passive systems coupled pairwise by heterogeneous, linear or nonlinear passive systems, including systems with memory such as memristive systems. The semi-passive systems are assumed to satisfy a certain input–output symmetry and can for instance be oscillators with an asymptotically stable limit cycle or systems with asymptotically stable equilibrium, but also chaotic systems or neuronal oscillators. We represent the system of coupled semi-passive systems by a graph. The semi-passive systems are associated with the nodes of that graph and the nonlinear passive systems are associated with the graphs edges. To each such system we associate a weight defined as the largest value w.r.t. which the system is input- or output-passive. We derive a sufficient condition for synchronization that is phrased in terms of the algebraic connectivity of the weighted coupling graph, a generalized one-sided Lipschitz-condition associated to the semi-passive system and a constant related to its linear input–output-behavior. We also derive a sufficient condition for output synchronization in a border-line case where our main condition is not applicable.https://doi.org/10.1007/s42452-025-07140-9Dissipative systemsSynchronizationNonlinear systemsMemristorsNetwork dynamics
spellingShingle Robin Lautenbacher
Jonas Röhrig
Karlheinz Ochs
Ralf Köhl
A sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systems
Discover Applied Sciences
Dissipative systems
Synchronization
Nonlinear systems
Memristors
Network dynamics
title A sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systems
title_full A sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systems
title_fullStr A sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systems
title_full_unstemmed A sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systems
title_short A sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systems
title_sort sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systems
topic Dissipative systems
Synchronization
Nonlinear systems
Memristors
Network dynamics
url https://doi.org/10.1007/s42452-025-07140-9
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