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<p>Polyrhythmicity is a core dynamical feature of central pattern generators (CPGs). In canonical models such as the 3-cell CPG, the multistable landscape has been exhaustively mapped using numerical methods like the Poincaré return maps. However, a systematic, first-principles explanation for why this specific landscape necessarily emerges is still lacking. To address this, this study investigates the dynamics of a multistable 3-cell CPG under release and escape mechanisms using phase response curve and interaction function. Our results show that under identical rhythmic patterns, release-type and escape-type CPGs exhibit starkly different phase response curve (PRC) shapes: the release-type PRC is dominated by a pronounced positive peak (phase advance), while the escape-type PRC features a deep negative trough (phase delay). Phase plane analysis of individual neurons reveals the dynamical mechanisms underlying these distinct PRC shapes. Furthermore, starting from the PRCs, we derive the network’s interaction function, establishing a two-dimensional phase difference system that describes the system’s dynamics. Analysis of the interaction function reveals that although the release and escape mechanisms correspond to opposite PRC shapes and symmetrically reversed phase flow structures, they possess identical fixed point configurations in the phase difference space. This explains why two opposing microscopic mechanisms (release and escape) give rise to the same macroscopic multistable patterns. The phase-dynamics framework developed in this work complements the phenomenological description provided by Poincaré return maps, thereby enriching the methodology for analyzing high-dimensional, multi-rhythmic CPG dynamics.</p>

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Dynamical analysis of multistable 3-cell CPG based on phase response curve and interaction function

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Qinghua Zhu,
  • Song Zheng,
  • Fang Han

摘要

Polyrhythmicity is a core dynamical feature of central pattern generators (CPGs). In canonical models such as the 3-cell CPG, the multistable landscape has been exhaustively mapped using numerical methods like the Poincaré return maps. However, a systematic, first-principles explanation for why this specific landscape necessarily emerges is still lacking. To address this, this study investigates the dynamics of a multistable 3-cell CPG under release and escape mechanisms using phase response curve and interaction function. Our results show that under identical rhythmic patterns, release-type and escape-type CPGs exhibit starkly different phase response curve (PRC) shapes: the release-type PRC is dominated by a pronounced positive peak (phase advance), while the escape-type PRC features a deep negative trough (phase delay). Phase plane analysis of individual neurons reveals the dynamical mechanisms underlying these distinct PRC shapes. Furthermore, starting from the PRCs, we derive the network’s interaction function, establishing a two-dimensional phase difference system that describes the system’s dynamics. Analysis of the interaction function reveals that although the release and escape mechanisms correspond to opposite PRC shapes and symmetrically reversed phase flow structures, they possess identical fixed point configurations in the phase difference space. This explains why two opposing microscopic mechanisms (release and escape) give rise to the same macroscopic multistable patterns. The phase-dynamics framework developed in this work complements the phenomenological description provided by Poincaré return maps, thereby enriching the methodology for analyzing high-dimensional, multi-rhythmic CPG dynamics.