Limit-Cycle Proliferation Under Parametric Delayed Feedback in a Conductance-Based Neuron: Bifurcation Landscape,...

Area of Science:

• Computational Neuroscience
• Neuromorphic Engineering
• Dynamical Systems Theory

Background:

• Single neurons can exhibit complex dynamics, including stable periodic orbits.
• Delayed feedback control is a technique used to stabilize unstable dynamics.
• Information storage in biological systems often relies on complex neural dynamics.

Purpose of the Study:

• To investigate the potential of a single Hodgkin-Huxley neuron with delayed feedback control for information storage.
• To characterize the types and number of stable periodic orbits achievable.
• To develop and validate protocols for writing, reading, and erasing information stored as orbits.

Main Methods:

• Utilized a single Hodgkin-Huxley neuron model with Pyragas-type delayed feedback control.
• Systematically swept the parameter plane (gain K, time delay τ) to identify stable periodic orbits.
• Developed a Pattern-Oriented Limit-cycle Decoder (POLD) for orbit identification.
• Established write, read, and erase protocols for single-symbol operations.

Main Results:

• Identified 207 distinct orbit types across 12 topological categories, enabling multi-symbol storage.
• Demonstrated reliable orbit writing with a median settling time of 13.9 ms.
• Achieved 100% accuracy in reading stored symbols using POLD from minimal data.
• Validated a complete write-read-erase cycle with high accuracy and no data decay over 50s.

Conclusions:

• Parametric delayed feedback control offers a viable mechanism for limit-cycle-based information storage in spiking neurons.
• The system demonstrates a validated 12-symbol memory capacity, with potential for up to 67 symbols.
• This work serves as a computational proof-of-principle for neuromorphic engineering applications.