Theoretical analysis demonstrates global attractivity of positive equilibria in nonautonomous Ricker models, indicating that local stability partially extends to time-varying dynamics.
This paper investigates the global attractivity of a nonautonomous discrete-time Ricker model. By constructing suitable Lyapunov functions, we establish sufficient conditions for the global attractivity of all solutions to its unique positive equilibrium. Our results partially generalize the autonomous principle that ‘local stability implies global stability’ to the nonautonomous setting. A gap remains between the derived conditions and the critical threshold in the autonomous case, pointing to an interesting direction for future research.
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Sun et al. (2026) studied this question.
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