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In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, $\ddot{x}+\alpha x\dot{x}+\beta x^3+\gamma…

Exactly Solvable and Integrable Systems · Physics 2009-04-13 R Gladwin Pradeep , V K Chandrasekar , M Senthilvelan , M Lakshmanan

It is well known that linear and non-linear dissipative port-Hamiltonian systems in finite dimensions admit an energy balance, relating the energy increase in the system with the supplied energy and the dissipated energy. The integrand in…

Analysis of PDEs · Mathematics 2024-05-29 Friedrich M. Philipp

The geometric approach to mechanics based on the Jacobi metric allows to easily construct natural mechanical systems which are integrable (actually separable) at a fixed value of the energy. The aim of the present paper is to investigate…

Chaotic Dynamics · Physics 2009-11-10 Giuseppe Pucacco , Kjell Rosquist

We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…

Dynamical Systems · Mathematics 2025-06-23 Philipp L. Kinon , Tobias Thoma , Peter Betsch , Paul Kotyczka

A $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer is a two-site discrete nonlinear Schr\"odinger equation with one site losing and the other one gaining energy at the same rate. In this paper, two four-parameter families of cubic…

Exactly Solvable and Integrable Systems · Physics 2015-09-02 I. V. Barashenkov , D. E. Pelinovsky , P. Dubard

When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…

Optimization and Control · Mathematics 2022-10-19 Shara Balakrishnan , Aqib Hasnain , Robert Egbert , Enoch Yeung

A characterisation of the generators of quantum stochastic cocycles of completely positive (CP) maps is given in terms of the complete dissipativity (CD) of its form-generator. The pseudo-Hilbert dilation of the stochastic form-generator…

Mathematical Physics · Physics 2007-05-23 V. P. Belavkin

In this manuscript, we present a mixed finite element discretization for a class of boundary-damped anisotropic port-Hamiltonian systems. Using a multiplier method, we demonstrate that the resulting approximation model uniformly preserves…

Numerical Analysis · Mathematics 2025-03-21 Luis A. Mora , Kirsten Morris

We present a gradient-based calibration algorithm to identify a port-Hamiltonian system from given time-domain input-output data. The gradient is computed with the help of sensitivities and the algorithm is tailored such that the structure…

Numerical Analysis · Mathematics 2023-01-06 Michael Günther , Birgit Jacob , Claudia Totzeck

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a…

Mathematical Physics · Physics 2012-02-28 Marko Seslija , Arjan van der Schaft , Jacquelien M. A. Scherpen

A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…

Quantum Physics · Physics 2009-11-11 V. G. Kupriyanov , S. L. Lyakhovich , A. A. Sharapov

Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time $(\mathcal{PT})$ symmetry that are best understood as systems with…

Quantum Physics · Physics 2022-03-22 Kaustubh S. Agarwal , Jacob Muldoon , Yogesh N. Joglekar

In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion…

Numerical Analysis · Mathematics 2017-06-28 Elena Celledoni , Eirik Hoel Høiseth

The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly…

Dynamical Systems · Mathematics 2025-11-26 Matthias Ehrhardt , Michael Günther , Daniel Ševčovič

This paper presents a systematic observer design methodology for a class of port-Hamiltonian (pH) systems with state-dependent input matrices. Such systems can model a wide range of electromechanical systems, including magnetic levitation…

Optimization and Control · Mathematics 2026-04-06 Filippo Ugolini , Ning Liu , Yongxin Wu , Yann Le Gorrec , Alessandro Macchelli

An energy-based modeling framework for the nonlinear dynamics of spatial Cosserat rods undergoing large displacements and rotations is proposed. The mixed formulation features independent displacement, velocity and stress variables and is…

Numerical Analysis · Mathematics 2026-05-11 Philipp L. Kinon , Simon R. Eugster , Peter Betsch

This paper provides a first contribution to port-Hamiltonian modeling of district heating networks. By introducing a model hierarchy of flow equations on the network, this work aims at a thermodynamically consistent port-Hamiltonian…

A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyse nonlinear dynamical systems brings new strategies for…

Fluid Dynamics · Physics 2019-03-12 Jeremy Parker , Jacob Page

This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…

Numerical Analysis · Mathematics 2023-07-24 Cecilia Pagliantini , Federico Vismara

We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band…

Computational Physics · Physics 2026-05-11 Yiming Pan , Jinze He , Jiapeng Yang , Zhiwei Fan