Resonance-Dependent Pattern Dynamics in a Neural Field for Spatial Coding.

Overview

1. Machine Life and Intelligence Research Center, Guangzhou University, Guangzhou 510006, China
2. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
3. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China

Abstract

Continuous representations in brain navigation system are manifested as spatially structured patterns of population activity, such as a single-peaked bump moving along a ring manifold in head-direction system and hexagonal lattice patterns underlying spatial representation in grid-cell systems. These phenomena are commonly modelled within the framework of continuous attractor networks (neural dynamical field), yet the mechanisms by which activation-function nonlinearities interact with connectivity structure to determine pattern selection and dynamics remain incompletely understood. This paper separately analyses the interactions between non-resonant and resonant modes using a multiscale unfolding approach. We show that, when the critical modes satisfy a resonance condition, the quadratic nonlinearity of the activation function induces a three-mode coupling that fundamentally alters the structure of the amplitude equations and becomes the dominant mechanism governing spatial pattern selection. Building on this analysis, we introduce a weak asymmetric component in the connectivity and analytically derive the resulting pattern drift velocity, which is subsequently confirmed by numerical simulations. Finally, we apply these dynamical mechanisms to input-driven scenarios, illustrating that similar dynamical mechanisms can account for activity-bump tracking in head-direction models and lattice translations in grid-cell models. Overall, this work provides an analytically tractable framework for studying pattern dynamics in neural field models relevant to spatial representations, and may inform biomimetic approaches to spatial representation and navigation.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Data Availability Statement

The data supporting the findings of this study are available from the corresponding author upon reasonable request. Code will be made available on request.

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 4 keywords, 1 funder, 36 references.

Cite

This paper

Chen, Y., Qian, Y., & Peng, J. (2026). Resonance-Dependent Pattern Dynamics in a Neural Field for Spatial Coding. Biomimetics (Basel, Switzerland), 11(4), 224. https://doi.org/10.3390/biomimetics11040224

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