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Global Bifurcations
Published in LM Pismen, Working with Dynamical Systems, 2020
Global analysis of a dynamical system aims at defining all kinds of bifurcations affecting either the number of attractors or their basin boundaries. We start with approaching this problem in a qualitative way, looking for all possible transitions among stationary states and periodic orbits. This qualitative picture is supported by numerics, continuing the study of the exothermic chemical reaction in the accompanying Mathematica notebook. Following this, we explore ways to approach global dynamics analytically. First, is studying dynamics in the vicinity of a degenerate bifurcation at the double-zero eigenvalue. Second, is the use of singular perturbations in systems with separated time scales, in particular, almost Hamiltonian systems.
GLOBAL ANALYSIS OF STOCHASTIC BIFURCATION IN UEDA SYSTEM
Published in W. Q. Zhu, G.Q. Cai, R.C. Zhang, Advances in Stochastic Structural Dynamics, 2003
Wei Xu, Qun He, Haiwu Rong, Tong Fang
Although the theory of stochastic bifurcation has been advanced to a new level in the last decade, there remain a lot of problems to be solved. Even ihc definition of stochastic bifurcation needs to be improved In this paper, we suggest an alternative definition for stochastic bifurcation based on the global analysis of a nonlinear dynamical system subject to combined determinislic and random excitations, which focuses on a sudden change in the character of the attractor of the dynamical system as the bifurcation parameter passes through a critical value.
Floating bridge response under combined ship collision, wind and wave loads
Published in Ships and Offshore Structures, 2023
Zihao Wang, Yanyan Sha, Jasna Bogunović Jakobsen
Due to the limitations on the commonly available computational resources for finite element simulations, the analyses of long floating bridges against ship collisions are simplified into two parts: local structural damage assessment and global bridge response analysis (Sha et al. 2019). A local model of impacted bridge section is usually defined with fixed boundary conditions to investigate the local structural damage during a collision event. Since the energy dissipation from the global bridge motion is not included, the local deformation and damage might be overestimated. Global analysis is commonly performed with two objectives: (1) to determine the global motion and other global responses including internal forces and moments, and (2) to obtain the energy dissipations in local and global responses. This study focuses on the global dynamic response of the floating bridge under multi-hazard scenarios, i.e. the external dynamics between the striking ship and the bridge is the emphasis in the simulations. It should be noted that by using the simplified ship-bridge system, the residual damage of both the ship and the struck pontoon can not be well captured. Only head-on collisions are considered in the current analyses.