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Related papers: Reduced Order Characterization of Nonlinear Oscill…

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A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…

Statistical Mechanics · Physics 2013-03-19 B. I. Lev , A. G. Zagorodny

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…

Numerical Analysis · Mathematics 2024-07-25 Konstantinos Vlachas , Konstantinos Tatsis , Konstantinos Agathos , Adam R. Brink , Eleni Chatzi

We show how spectral submanifold theory can be used to construct reduced-order models for harmonically excited mechanical systems with internal resonances. Efficient calculations of periodic and quasi-periodic responses with the…

Dynamical Systems · Mathematics 2022-08-09 Mingwu Li , Shobhit Jain , George Haller

This article presents an adaptive nonlinear delayed feedback control scheme for stabilizing the unstable periodic orbit of unknown fractional-order chaotic systems. The proposed control framework uses the Lyapunov approach and sliding mode…

Systems and Control · Electrical Eng. & Systems 2023-11-10 Bahram Yaghooti , Kaveh Safavigerdini , Reza Hajiloo , Hassan Salarieh

Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear…

Mesoscale and Nanoscale Physics · Physics 2023-04-05 Ata Keşkekler , Vincent Bos , Alejandro M. Aragón , Peter G. Steeneken , Farbod Alijani

Spontaneous oscillations induced by time delays are observed in many real-world systems. Phase reduction theory for limit-cycle oscillators described by delay-differential equations (DDEs) has been developed to analyze their synchronization…

Adaptation and Self-Organizing Systems · Physics 2020-07-23 Kiyoshi Kotani , Yutaro Ogawa , Sho Shirasaka , Akihiko Akao , Yasuhiko Jimbo , Hiroya Nakao

We consider low-order controller design for large-scale linear time-invariant dynamical systems with inputs and outputs. Model order reduction is a popular technique, but controllers designed for reduced-order models may result in unstable…

Optimization and Control · Mathematics 2018-03-20 Peter Benner , Tim Mitchell , Michael L. Overton

The increasing penetration of renewable energy sources, characterised by low inertia and intermittent disturbances, presents substantial challenges to power system stability. As critical indicators of system stability, frequency dynamics…

Systems and Control · Electrical Eng. & Systems 2025-02-19 Xiao Li , Xinyi Wen , Benjamin Schäfer

A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…

Computational Engineering, Finance, and Science · Computer Science 2021-01-01 Malte Krack , Lars Panning-von Scheidt , Jörg Wallaschek

The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…

Dynamical Systems · Mathematics 2026-01-01 Zeray Hagos Gebrezabher

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now…

Neurons and Cognition · Quantitative Biology 2013-02-05 Kyle C A Wedgwood , Kevin K Lin , Rüdiger Thul , Stephen Coombes

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…

Statistical Mechanics · Physics 2023-10-27 Niccolò Zagli , Grigorios A. Pavliotis , Valerio Lucarini , Alexander Alecio

Many robotic systems are underactuated, meaning not all degrees of freedom can be directly controlled due to lack of actuators, input constraints, or state-dependent actuation. This property, compounded by modeling uncertainties and…

Systems and Control · Electrical Eng. & Systems 2025-10-10 Daniel M. Cherenson , Dimitra Panagou

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…

Numerical Analysis · Mathematics 2021-09-22 Alessandra Vizzaccaro , Andrea Opreni , Loïc Salles , Attilio Frangi , Cyril Touzé

This paper presents a new model-based algorithm that computes predictive optimal controls on-line and in closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive,…

Robotics · Computer Science 2017-09-04 Alex Ansari , Todd Murphey

We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…

Numerical Analysis · Mathematics 2016-02-17 Alessandro Alla , J. Nathan Kutz

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

Computational Physics · Physics 2023-08-09 Cheng Huang , Karthik Duraisamy

We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…

Dynamical Systems · Mathematics 2022-06-03 Dohyun Kim , Hansol Park

In this paper we use the parameterization method to provide a complete description of the dynamics of an $n$-dimensional oscillator beyond the classical phase reduction. The parameterization method allows, via efficient algorithms, to…

Dynamical Systems · Mathematics 2021-01-22 Alberto Pérez-Cervera , Tere M. Seara , Gemma Huguet

A major goal for reduced-order models of unsteady fluid flows is to uncover and exploit latent low-dimensional structure. Proper orthogonal decomposition (POD) provides an energy-optimal linear basis to represent the flow kinematics, but…

Fluid Dynamics · Physics 2022-03-23 Jared L. Callaham , Steven L. Brunton , Jean-Christophe Loiseau