Multiple Monotone Stationary Fronts for Discrete Bistable Systems on Pinning Interval

• Wen-Xin Qin ^[1] ; Tong Zhou ^[2]
  1. [1] Soochow University

     Soochow University

     China

     
  2. [2] Suzhou University of Science and Technology

     Suzhou University of Science and Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 5, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We study the multiplicity of monotone stationary fronts for spatially discrete bistable systems. Let A < B be two critical values such that the system has three homogeneous equilibria if the driving force F ∈ (A, B). It is well-known that there exist transition thresholds F−c≤ F+c of the driving force such that there are monotone stationary fronts but no travelling fronts for F−c≤ F ≤ F+c and travelling fronts but no monotone stationary fronts if A < F < F−c or F+c < F < B. In this paper, we prove using some recent results on the depinning force that there exist at least two distinct (up to translation) monotone stationary fronts as long as propagation failure occurs.

    Moreover, we construct infinitely many stationary multi-hump solutions which are left- and right-asymptotic to two different homogeneous equilibria.

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