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January 26, 2026International Journal of Biomathematics

Spatio-temporal dynamics of relaxation oscillations in a reaction-diffusion-ODE system

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Authors

LHLingling Hou

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Overview

This investigation reveals rhythmic patterns in a reaction-diffusion system, suggesting new insights for biological oscillations.

Key Points

  • The aim is to explore the emergence of relaxation oscillations and periodic solutions in a reaction-diffusion system inspired by biological models.
  • Analyzed a reaction-diffusion-ODE system inspired by FitzHugh-Nagumo model.
  • Applied multiple time scale analysis to establish the existence of relaxation oscillations.
  • Utilized Hopf bifurcation theory to derive regular periodic solutions.
  • Extended analysis to spatial domains to characterize pattern formation.
  • Established the existence of relaxation oscillations critical for rhythmic biological phenomena.
  • Derived regular periodic solutions through Hopf bifurcation across distinct parameter regimes.
  • Characterized both spatially homogeneous and inhomogeneous periodic solutions.
  • Simulations indicated a variety of dynamics, including discontinuous states and quasi-periodic patterns.

Cite This Study

Lingling Hou (2026) studied this question.

synapsesocial.com/papers/69770353722626c4468e854chttps://doi.org/10.1142/s1793524526500075
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