Dynamic analysis of a stage-structured forest population model with non-smooth continuous threshold harvesting

Abstract

In this article, we develop a delayed tree population model with non-smooth continuous threshold harvesting. By carefully addressing the main difficulty caused by the nonlinear term and the time delay together, the existence and number of the positive equilibrium points are classified. Taking full use of the domain-decomposition method and Hopf bifurcation theory, the stability of the model, including local and global asymptotic stability of the equilibria, bistability and stability switches occurring at the positive equilibrium, is analyzed relatively completely. This is followed by an investigation of the influence of the maturation delay of trees on the optimal harvesting. Numerical analysis illustrates that the model gives rise to chaotic-like oscillations through period doubling with the increase of the maturation delay or the harvesting rate and undergoes long transients and regime shifts. Even, the maturation delay can induce multi-types of tristability.