Optimal control of a discrete-time plant–herbivore/pest model with bistability in fluctuating environments

Sunmi Lee, Chang Yong Han, Minseok Kim, Yun Kang

    Research output: Contribution to journalArticlepeer-review

    1 Scopus citations


    Motivated by regulating/eliminating the population of herbivorous pests, we investigate a discrete-time plant–herbivore model with two different constant control strategies (removal versus reduction), and formulate the corresponding optimal control problems when its dynamics exhibits varied types of bi-stability and fluctuating environments. We provide basic analysis and identify the critical factors to characterize the optimal controls and the corresponding plant–herbivore dynamics such as the control upper bound (the effectiveness level of the implementation of control measures) and the initial conditions of the plant and herbivore. Our results show that optimal control could be easier when the model has simple dynamics such as stable equilibrium dynamics under constant environment or the model exhibits chaotic dynamics under fluctuating environments. Due to bistability, initial conditions are important for optimal controls. Regardless of with or without fluctuating environments, initial conditions taken from the near the boundary makes optimal control easier. In general, the pest is hard to be eliminated when the control upper bound is not large enough. However, as the control upper bound is increased or the initial conditions are chosen from near the boundary of the basin of attractions, the pest can be manageable regardless of the fluctuating environments.

    Original languageEnglish (US)
    Pages (from-to)5075-5103
    Number of pages29
    JournalMathematical Biosciences and Engineering
    Issue number5
    StatePublished - 2022


    • bi-stability
    • discrete optimal control theory
    • discrete plant–herbivore system
    • fluctuating environments

    ASJC Scopus subject areas

    • Modeling and Simulation
    • General Agricultural and Biological Sciences
    • Computational Mathematics
    • Applied Mathematics


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