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Stochastic stability of synchronized states in time-delayed Kuramoto oscillators: From all-to-all to ring topology
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DOI：10.1016/j.physa.2026.131780.png)
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Abstract
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Time delay fundamentally enriches the dynamics of coupled oscillator networks, giving rise to multistability between synchronized and incoherent states. Here we investigate how time delay and coupling strength jointly shape the stochastic stability of synchronized states in time-delayed Kuramoto oscillators, under both all-to-all and ring network topologies. Using mean first-passage time measurements and quasipotential theory, we show that the quasipotential framework extends naturally to these infinite-dimensional nongradient systems. For both topologies, coupling strength consistently deepens the quasipotential well, while time delay acts as a key destabilizing factor that systematically reduces the barrier height. For sufficiently large delays, the synchronized state becomes so weakly stable that the slope of the linear fit can no longer reliably serve as a proxy for the quasipotential barrier height, and a more complete characterization requires accounting for the prefactor of the exponential scaling. These findings reveal the distinct and opposing roles of coupling strength and time delay in shaping stochastic stability across different network topologies.
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