A SURVEY OF CONSTRUCTING LYAPUNOV FUNCTIONS FOR MATHEMATICAL MODELS IN POPULATION BIOLOGY

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Global Stability of Infectious Disease Models Using Lyapunov Functions (2013, methodology): “The method of Lyapunov functions is commonly used to establish global stability results for biological models; see, for example, [15, 23] for general theory of Lyapunov functions and [8, 20, 21] for applications in mathematical biology.”
Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ✩ (2009, background): “On the other hand, we have the following global stability theorem about (λ, vλ), which is essentially known [21] but we include here for the sake of completeness:”
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics (2016, background): “[12] for more details on the construction of Lyapunov functionals, and [5, 29, 43] for an independent proof based on comparison arguments).”
Global Dynamics of the Lotka‐Volterra Competition‐Diffusion System: Diffusion and Spatial Heterogeneity I (2016, background): “10) is discussed in [11, 21], which can be applied to prove Theorem 3.”
Cross-diffusion induced Turing instability for a three species food chain model (2012, methodology): “More methods of constructing Lyapunov function can be found in Hsu’s paper [10].”