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Updated: Jun 25, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
From networks of unstable attractors to heteroclinic switching
1Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37073 Göttingen, Germany.
Abstract:
We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each other's basin volume. This counterintuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed interactions. We analytically show that upon continuously removing a local noninvertibility of the system, the two unstable attractors become a set of two nonattracting saddle states that are heteroclinically connected. This transition equally occurs from larger networks of unstable attractors to heteroclinic structures and constitutes a new type of singular bifurcation in dynamical systems.
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