Chaotic behavior and multistability of a tree trunk structure driven by self-and parametric hydrodynamic forces

Abstract This study investigates the chaotic behavior of a tree trunk under dynamic wind loads, focusing on control strategies and multistability. We consider time-varying wind speeds and analyze a specific case where hydrodynamic drag forces align with the flow velocity. The stability of the model’s equilibrium points is analyzed theoretically and numerically. Melnikov’s method is employed to identify conditions for homoclinic bifurcation. Numerical simulations employing basin of attraction confirm the analytical predictions. Our findings show a decrease in the threshold for chaos with increasing amplitudes of external excitation, damping coefficient, and parametric damping. The global dynamics are explored numerically using a fourth-order Runge-Kutta method. When solely subjected to external excitation, the system exhibits period doubling bifurcations, multiperiodic oscillations, mixed-mode oscillations, and chaos. Conversely, with self- and parametric drag forces, the system displays reverse periodic bifurcations, periodic bubbling oscillations, antimonotonicity, transient chaos, and chaos. Poincaré maps analyze the geometric structure of chaotic attractors, revealing a strong influence of dimensionless drag parameters. These parameters can be manipulated to control or eliminate chaos. Furthermore, the system exhibits multistability, with coexisting attractors. Beyond its application in protecting infrastructure from wind damage, this research can contribute to ecological balance by improving our understanding of tree wind resistance.