# gst: singular bifurcations, an approach

<< Bifurcation analysis is traditionally based on the assumption of a regular perturbative expansion, close to the bifurcation point, in terms of a variable describing the passage of a system from one state to another. However, it is shown that a regular expansion is not the rule due to the existence of hidden singularities in many models, paving the way to a new paradigm in nonlinear science, that of singular bifurcations. The theory is first illustrated on an example borrowed from the field of active matter (phoretic microswimers), showing a singular bifurcation. >>

AA << then present a universal theory on how to handle and regularize these bifurcations, bringing to light a novel facet of nonlinear sciences that has long been overlooked. >>️

Alexander Farutin, Chaouqi Misbah. Singular bifurcations and regularization theory. Phys. Rev. E 109, 064218. Jun 27, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064218

Alexander Farutin, Chaouqi Misbah. Singular Bifurcations : a Regularization Theory. arXiv: 2112.12094v2 [cond-mat.soft]. Jan 6, 2022. 

https://arxiv.org/abs/2112.12094 

Also: transition, singularity, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, singularity, bifurcation

# gst: distance to criticality in unknown noise

<< real-world systems are often corrupted by unknown levels of noise that can distort (..) temporal signatures. Here (AA) aim to develop noise-robust indicators of the distance to criticality (DTC) for systems affected by dynamical noise in two cases: when the noise amplitude is either fixed or is unknown and variable across recordings. >>️

<< in the variable-noise setting, where (..) conventional indicators perform poorly, (AA) highlight new types of high-performing time-series features and show that their success is accomplished by capturing the shape of the invariant density (which depends on both the DTC and the noise amplitude) relative to the spread of fast fluctuations (which depends on the noise amplitude). (AA) introduce a new high-performing time-series statistic, the rescaled autodensity (RAD). >>️

Brendan Harris, Leonardo L. Gollo, Ben D. Fulcher. Tracking the Distance to Criticality in Systems with Unknown Noise. Phys. Rev. X 14, 031021. Aug 8, 2024.

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.031021

Also: noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, criticality, bifurcation, noise, transition

# gst: networks of pendula with diffusive interactions, chaotic regime seems to emerge at low energies.

AA << study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian; as such, the energy is conserved. >>️

<< The behaviour observed showcases a mechanism for the appearance of chaotic oscillations in conservative systems. For Hamiltonians with two degrees of freedom, it has been shown how chaos can emerge near a saddle-centre equilibrium possessing a homoclinic orbit. (AA) have seen that higher-dimensional systems having mixed equilibria, i.e., generalisations of a saddle-center where the eigenvalues are only imaginary and reals, also show chaotic behaviour close to those points.  >>️

AA << complement the analysis with some numerical simulations showing the interplay between bifurcations of the origin and transitions to chaos of nearby orbits. A key feature is that the observed chaotic regime emerges at low energies. >>

️

Riccardo Bonetto, Hildeberto Jardón-Kojakhmetov, Christian Kuehn. Networks of Pendula with Diffusive Interactions. arXiv: 2408.02352v1 [math.DS]. Aug 5, 2024.

https://arxiv.org/abs/2408.02352

Also: pendulum, network, transition, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, pendulum, network, transition, chaos, bifurcation

# gst: shape-shifting architecture inspired by metamorphosis, the metamorphosis kirigami system.

<< Kirigami is a variation of origami that involves cutting and folding paper. But while kirigami traditionally uses two-dimensional materials, Yin (Jie Yin) applies the same principles to three-dimensional materials. The metamorphosis system starts with a single unit of 3D kirigami. Each unit can form multiple shapes in itself. But these units are also modular—they can be connected to form increasingly complex structures. Because the individual units themselves can form multiple shapes, and can connect to other units in multiple ways, the overall system is capable of forming a wide variety of architectures. >>

<< The system we've developed was inspired by metamorphosis, (..) With metamorphosis in nature, animals change their fundamental shape. We've created a class of materials that can be used to create structures that change their fundamental architecture. (..) Think of what you can build with conventional materials, (..) Now imagine what you can build when each basic building block is capable of transforming in multiple ways.  (..) The metamorphosis kirigami system does not allow you to disassemble a structure, (..) And because the sides of each cubic unit are rigid and fixed at 90-degree angles, the assembled structure does not bend or flex very much. However, the finished structure is capable of transforming into different architectures.>> Jie Yin.️

Matt Shipman. Inspired by metamorphosis, researchers create materials for shape-shifting architecture. North Carolina State University. Sep 08, 2021. 

https://phys.org/news/2021-09-metamorphosis-materials-shape-shifting-architecture.html  

Yanbin Li, Jie Yin. Metamorphosis of three-dimensional kirigami-inspired reconfigurable and reprogrammable architected matter. Materials Today Physics, 21, 100511. doi: 10.1016/ j.mtphys.2021.100511.

https://www.sciencedirect.com/science/article/abs/pii/S2542529321001723

Also

keyword 'origami' in FonT

https://flashontrack.blogspot.com/search?q=origami

Keywords: gst, origami, kirigami, architecture, bifurcation, metamorphosis,  reconfigurability, reprogrammability.