Related papers: A contraction based, singular perturbation approac…
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…
We investigate combinatorial dynamical systems on simplicial complexes considered as {\em finite topological spaces}. Such systems arise in a natural way from sampling dynamics and may be used to reconstruct some features of the dynamics…
We present data-based conditions for enforcing contractivity via feedback control and obtain desired asymptotic properties of the closed-loop system. We focus on unknown nonlinear control systems whose vector fields are expressible via a…
We investigate the possible origin of hierarchical structures in complex systems describable in terms of a finite and small number of parameters which control the behavioral pattern at each level of organization. We argue that the…
We study stability of interacting nonlinear systems with time-delayed communications, using contraction theory and a simplified wave variable design inspired by robotic teleoperation. We show that contraction is preserved through specific…
This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling…
With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
To characterize the complex higher-order interactions among variables within a system, this study introduces a novel framework, termed System Information Decomposition (SID), aimed at decomposing the information entropy of variables into…
Examining individual components of cellular systems has been successful in uncovering molecular reactions and interactions. However, the challenge lies in integrating these components into a comprehensive system-scale map. This difficulty…
Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
We study the simplest mode-coupling equation which describes the time correlation function of the spherical p-spin glass model. We formulate a systematic perturbation theory near the mode-coupling transition point by introducing multiple…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
A module $M$ is {called} stable if it has no nonzero projective direct summand. For a ring $ R $, we study conditions under which $R$-modules from certain classes decompose as a direct sum of a projective submodule and a stable submodule.…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum and spin variables $[X, P,…
Within the decoherence theory we investigate the physical background of the condition of the separability (diagonalizability in noncorrelated basis) of the interaction Hamiltonian of the composite system, "system plus environment". It…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
The contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of integrability.