TITLE:
Bursting and Mixed-Mode Oscillations of a Tree Trunk Structure Driven by Self and Parametric Aerodynamic Forces
AUTHORS:
Charles Adéyèm, Adébiyi Joseph Adéchinan
KEYWORDS:
Tree Trunk, Aerodynamic Drag Force, Bursting Oscillations, Mixed-Mode Oscillations, Coexisting Attractors
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.15 No.12,
December
29,
2025
ABSTRACT: This paper addresses the existence of bursting phenomena and mixed-mode oscillations (MMOs) in a tree trunk structure subjected to external excitation, particularly when the aerodynamic drag force is in the same direction as the flow velocity and the trunk velocity remains lower than that of the wind. A mathematical model based on Newton’s second law has been developed to represent the mechanical behavior of the tree trunk. The behavior of the considered system is studied using bifurcation diagrams, Lyapunov exponent diagrams, time histories, and phase portraits. The global dynamics are explored numerically using the fourth-order Runge-Kutta method. The results reveal that our system exhibits bursting oscillations, mixed-mode oscillations, and coexisting attractors. Understanding the phenomena that appear in the system under study could help to better assess the risk of tree failure by identifying critical conditions, evaluating tree stability, and detecting potential failure modes. Both phenomena can help better predict critical conditions and improve risk management in forestry and urban environments.