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May 24, 2026Journal of Physics CommunicationsOpen Access

Parameter-driven stability and equilibria analysis of a coupled Allen–Cahn system

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Authors

MFMostafa Fazly

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Overview

Randomized trial examines stability in coupled Allen-Cahn systems, indicating impacts on equilibria classification.

Key Points

  • This research aims to analyze the stability and equilibria of a coupled Allen-Cahn system with varying coupling parameters.
  • Examined a coupled Allen-Cahn system with two components and specific coupling parameters (λ, γ) > 0.
  • Classified critical points and identified nontrivial equilibria for λγ ≠ 1, and analyzed for continuity when λ = γ = 1.
  • Conducted stability analysis and numerical visualizations of equilibrium maps and phase-plane vector fields.
  • Identified asymptotic stability for coupling parameters λγ < 1 and instability for λγ > 1.
  • Categorized steady states as either center or saddle based on the coupling regime.
  • Provided numerical illustrations of how stability and bifurcation patterns differ across the (λ, γ)-plane.

Cite This Study

Mostafa Fazly (2026) studied this question.

synapsesocial.com/papers/6a12949848a0ea1665671063https://doi.org/10.1088/2399-6528/ae6bfd
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Stability and Robustness of Time-discretization Schemes for the Allen-Cahn Equation via Bifurcation and Perturbation Analysis2024
  2. 2Uncertainty quantification analysis of bifurcations of the Allen--Cahn equation with random coefficients2024
  3. 3Bifurcation analysis, and exact solutions of the two-mode Cahn–Allen equation by a novel variable coefficient auxiliary equation method2024 · 9 citations
  4. 4Equilibrium and stability of coupled nonlinear energy-storing components2026
  5. 5Borel control and efficient numerical techniques to solve the Allen–Cahn equation governed by temporal multiplicative noise2024