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Multiscale Ordinal-Pattern Dynamics and Temporal Symmetries in a Photonic Neuron with Single and Dual Delayed

Julian Feiveson¹, Mateu Yearian¹, Maddie Jones¹

¹Physics Department, Whitman College, Walla Walla, WA 99362, USA.

Entropy (Basel, Switzerland)

|May 26, 2026

Summary

Complex photonic neuron dynamics with multiple timescales were analyzed. Ordinal analysis revealed universal hidden symmetries across different feedback configurations, highlighting multiscale organization.

Keywords:

chaos complex dynamics emergence multiscale dynamics photonic neuron

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Area of Science:

Physics
Nonlinear Dynamics
Complex Systems

Background:

Complex dynamical systems often exhibit feedback delays and multiple timescales.
Interactions between fast and slow dynamics lead to emergent behaviors not seen in single-timescale systems.
Photonic neurons are key components in advanced optical and neural network systems.

Purpose of the Study:

Investigate how coupled fast and slow timescales influence the dynamics of a photonic neuron.
Analyze the impact of single and dual delayed feedback on system behavior.
Characterize temporal correlations and symmetry properties across different timescales.

Main Methods:

Utilized ordinal pattern analysis and ordinal-based complexity measures.
Examined fast peaks and slow spikes generated by the photonic neuron.
Applied symmetry-based Φ-space representation to analyze system dynamics.

Main Results:

Signatures of determinism differed significantly between fast and slow timescales.
A strong multiscale organization of dynamics was revealed.
All system states, regardless of timescale or feedback, collapsed onto a common curve in Φ-space.

Conclusions:

A universal structure governs the photonic neuron's dynamics across temporal scales and feedback types.
Underlying constraints dictate system behavior, irrespective of complexity.
Ordinal-based methods effectively uncover hidden symmetries and multiscale organization in delayed nonlinear systems.