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<p>In this paper, we consider a class of bore-like wave models and analyze the dynamics of simplified Burgers-type equation. Traveling wave reduction produces a Liénard equation, enabling geometric characterization of equilibrium distributions. Phase plane analysis reveals trajectory topology evolution across parameter regimes. Near degenerate equilibria, center manifold theory enables dimension reduction, while Hopf bifurcation theory identifies limit cycle generation thresholds. Liénard’s theorem ultimately establishes global asymptotic stability in phase space.</p>

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Dynamic analysis of the Liénard system for bore-like flows

  • 期刊论文

  • 发表日期：

    2025年10月23日

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  • Wanli Tian,
  • JinRong Wang

摘要

In this paper, we consider a class of bore-like wave models and analyze the dynamics of simplified Burgers-type equation. Traveling wave reduction produces a Liénard equation, enabling geometric characterization of equilibrium distributions. Phase plane analysis reveals trajectory topology evolution across parameter regimes. Near degenerate equilibria, center manifold theory enables dimension reduction, while Hopf bifurcation theory identifies limit cycle generation thresholds. Liénard’s theorem ultimately establishes global asymptotic stability in phase space.