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Nami Mogharabin and Amin Ghadami J. Comput. Nonlinear Dynam. Feb 2025, 20(2): 021006 https://doi.org/10.1115/1.4067297 Characterizing the nonlinear behavior of dynamical systems near the stability boundary is a critical step toward understanding, designing, and controlling systems prone to stability concerns. Traditional methods for bifurcation analysis in both experimental systems and large-dimensional models are often hindered either by the absence of an accurate model or by the analytical complexity involved. This paper presents a novel approach that combines the theoretical frameworks of nonlinear reduced-order modeling and stability analysis with advanced machine learning techniques to perform bifurcation analysis in dynamical systems. By focusing on a low-dimensional nonlinear invariant manifold, this work proposes a data-driven methodology that simplifies the process of bifurcation analysis in dynamical systems. The core of our approach lies in utilizing carefully designed neural networks to identify nonlinear transformations that map observation space into reduced manifold coordinates in its normal form where bifurcation analysis can be performed. The unique integration of analytical and data-driven approaches in the proposed method enables the learning of these transformations and the performance of bifurcation analysis with a limited number of trajectories. Therefore, this approach improves bifurcation analysis in model-less experimental systems and cost-sensitive high-fidelity simulations. The effectiveness of this approach is demonstrated across several examples. 
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Complex Modal Synthesis Method for Viscoelastic Flexible Multibody System Described by ANCF1/24/2025 Zuqing Yu, Zhuo Liu, Yu Wang, and Qinglong Tian J. Comput. Nonlinear Dynam. Mar 2025, 20(3): 031004 https://doi.org/10.1115/1.4067522 The viscoelastic dynamic model of flexible multibody coupled with large rotation and deformation can be described by the absolute nodal coordinate formulation (ANCF). However, with the increase of degrees-of-freedom, the computational cost of viscoelastic multibody systems will be very high. In addition, for nonproportionally viscoelastic flexible multibody systems, the orthogonality and superposition of complex modes only exist in the state space. In this investigation, a systematical procedure of model reduction method for viscoelastic flexible multibody systems described by ANCF is proposed based on the complex modal synthesis method. First, the whole motion process of the system is divided into a series of quasi-static equilibrium configurations. Then the dynamic equation is locally linearized based on the Taylor expansion to obtain the constant tangent stiffness matrix and damping matrix. The initial modes and modal coordinates need to be updated for each subinterval. A modal selection criterion based on the energy judgment is proposed to ensure the energy conservation and accuracy by the minimum number of truncations. Finally, three numerical examples are carried out as verification. Simulation results indicate that the method proposed procedure reduces the system scale and improves the computational efficiency under the premise of ensuring the simulation accuracy. 
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N'Gbo N'Gbo, Changpin Li, and Min Cai J. Comput. Nonlinear Dynam. Mar 2025, 20(3): 031002. https://doi.org/10.1115/1.4067471 This article focuses on investigating fractional Lyapunov exponents for generalized ψψ-fractional differential systems. By employing a new and more suitable definition, we derive an expression for the fractional Lyapunov exponents using the inverse of the Mittag-Leffler function, which depends on the kernel, weight, and order of the considered fractional derivative. We also provide an upper bound for the obtained fractional Lyapunov exponents that is tighter than the one available in existing literature. Finally, experiments conducted on a hyperchaotic 5D system and the well-known Lorenz system serve to illustrate and verify our main results.  |
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