第145回

日時 Time

2026年10月30日（金）16:30–18:00

場所 Place

金沢大学自然科学5号館数学棟4階コロキウム＋Zoom（ハイブリッド）
Zoom 登録リンク：https://kanazawa-university.zoom.us/meeting/register/cENPgW_RTIqmVZYySF93Gw

講演者 Speaker

齋藤 保久（島根大学）

タイトル Title

Lyapunov functionals for delay-independent global stability in two-dimensional Lotka–Volterra systems with distributed delays

概要 Abstract

Lotka–Volterra systems constitute one of the fundamental classes of models in population dynamics, and the global stability of delayed Lotka–Volterra systems has been extensively studied. In this talk, we consider a general two-dimensional Lotka–Volterra system with distributed delays and investigate conditions under which a positive equilibrium is globally asymptotically stable independently of the size and distribution of the delays.
For this problem, Faria (2009) established a sharp necessary and sufficient condition based on the structure of the coefficient matrices. On the other hand, Lyapunov functionals provide a powerful and direct approach to the global behavior of solutions, although their construction is generally far from systematic. It is therefore natural to ask to what extent the known sharp stability condition can be recovered through an explicitly constructed Lyapunov functional. In this talk, we construct such a functional by exploiting the two-dimensional structure of the system and derive a delay-independent sufficient condition for global asymptotic stability. We then compare this condition with the known sharp criterion and characterize precisely when the two conditions coincide. When they do not coincide, we further quantify their deviation and discuss the sharpness and limitations of the Lyapunov-functional approach.