arXiv subjects

Andreas Amann

Publications and source records attributed to Andreas Amann.

At least 19 recordsLinked to original sources

arXiv2025

Delayed Interactions in Active Agents: Stability and Formations

Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs) that incorporate inertial effects. In this paper, we investigate the stability of pattern formation of active agents with inertia and time delays, in both uncoupled and coupled scenarios. We derive and analyze a high-dimensional linear DDE model that characterizes the stability of such formations. Starting with the uncoupled scenario, where agents are driven only by a virtual leader, we describe the stability spectrum and provide conditions for the delay-independent (absolute) stability of the formations, as well as delay-dependent stability and unstable hyperbolic behavior. Different cases correspond to distinct universality classes of the corresponding spectrum. For the coupled scenario, where agents are driven by both the virtual leader and inter-agent interactions, we consider both symmetric and non-symmetric coupling topologies. Here we also provide an explicit spectrum classification, including the absolute stability criterion. Additionally, we investigate interactions in the large-delay limit, where delays affect inter-agent coupling, while local feedback remains instantaneous. In this limit, we prove rigorously that the stability region in the complex plane of the eigenvalues of the Laplacian matrix converges to a circle centered at the origin, a phenomenon previously observed in delay-coupled networks. Our findings provide a universal framework for understanding stable formations and motions of active agents with delayed interactions.

math.DS↗

arXiv2024

Synchronization cluster bursting in adaptive oscillators networks

Adaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our numerical observations reveal the emergence of synchronization cluster bursting, characterized by periodic transitions between cluster synchronization and global synchronization. By investigating a reduced model, the mechanisms underlying synchronization cluster bursting are clarified. We show that a minimal model exhibiting this phenomenon can be reduced to a phase oscillator with complex-valued adaptation. Furthermore, the adaptivity of the system leads to the appearance of additional symmetries and thus to the coexistence of stable bursting solutions with very different Kuramoto order parameters.

nlin.AO↗

arXiv2024

Exploring the origins of switching dynamics in a multifunctional reservoir computer

The concept of multifunctionality has enabled reservoir computers (RCs), a type of dynamical system that is typically realised as an artificial neural network, to reconstruct multiple attractors simultaneously using the same set of trained weights. However there are many additional phenomena that arise when training a RC to reconstruct more than one attractor. Previous studies have found that, in certain cases, if the RC fails to reconstruct a coexistence of attractors then it exhibits a form of metastability whereby, without any external input, the state of the RC switches between different modes of behaviour that resemble properties of the attractors it failed to reconstruct. In this paper we explore the origins of these switching dynamics in a paradigmatic setting via the `seeing double' problem.

math.DS↗

arXiv2023

Time resolved eye diagrams to exploit hidden high energy branches in a nonlinear wideband vibration energy harvester

A wideband vibration energy harvester with multiple nonlinear forces is investigated. The nonlinearities are due to repulsive magnets and hardening springs, which gives rise to multistabilities between a number of energy branches. Not all branches are accessible by a simple up or down sweep of the driving frequency and in particular the highest energy branch is often hidden, requiring a suitable frequency schedule to be accessed. Detailed theoretical understanding of the energy branch structure along with robust experimental methods are essential for characterizing each of the energy branches to enhance the energy output from such vibration energy harvesting system. We introduce a graphical representation in the form of eye diagrams based on time-resolved measurements of acceleration and output voltage to study the dynamical features of the different branches. This generic approach allows us to optimize the design, which results in 1.3mW of power generated at 1g over 44Hz frequency bandwidth while maintaining a small footprint of $1.23 cm^3$. The energy conversion ratio of the energy harvester at 120Hz drive frequency is 0.52 for the high energy branch.

physics.app-ph↗

arXiv2023

Dynamics of a time-delayed relay system

We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of the parameters. We present a detailed study of these periodic solutions and their bifurcations. Starting from an integro-differential model, we show how to reduce the system to a set of finite-dimensional maps. We then demonstrate that the parameter regions of existence of periodic solutions can be understood in terms of discontinuity induced bifurcations and their stability is determined by smooth bifurcations. Using this technique we are able to show that slowly oscillating solutions are always stable if they exist. We also demonstrate the coexistence of stable periodic solutions with quasiperiodic solutions.

math.DS↗

arXiv2023

Multifunctionality in a Connectome-Based Reservoir Computer

Multifunctionality describes the capacity for a neural network to perform multiple mutually exclusive tasks without altering its network connections; and is an emerging area of interest in the reservoir computing machine learning paradigm. Multifunctionality has been observed in the brains of humans and other animals: particularly, in the lateral horn of the fruit fly. In this work, we transplant the connectome of the fruit fly lateral horn to a reservoir computer (RC), and investigate the extent to which this 'fruit fly RC' (FFRC) exhibits multifunctionality using the 'seeing double' problem as a benchmark test. We furthermore explore the dynamics of how this FFRC achieves multifunctionality while varying the network's spectral radius. Compared to the widely-used Erd\"os-Renyi Reservoir Computer (ERRC), we report that the FFRC exhibits a greater capacity for multifunctionality; is multifunctional across a broader hyperparameter range; and solves the seeing double problem far beyond the previously observed spectral radius limit, wherein the ERRC's dynamics become chaotic.

cs.LG↗

arXiv2023

Seeing double with a multifunctional reservoir computer

Multifunctional biological neural networks exploit multistability in order to perform multiple tasks without changing any network properties. Enabling artificial neural networks (ANNs) to obtain certain multistabilities in order to perform several tasks, where each task is related to a particular attractor in the network's state space, naturally has many benefits from a machine learning perspective. Given the association to multistability, in this paper we explore how the relationship between different attractors influences the ability of a reservoir computer (RC), which is a dynamical system in the form of an ANN, to achieve multifunctionality. We construct the `seeing double' problem to systematically study how a RC reconstructs a coexistence of attractors when there is an overlap between them. As the amount of overlap increases, we discover that for multifunctionality to occur, there is a critical dependence on a suitable choice of the spectral radius for the RC's internal network connections. A bifurcation analysis reveals how multifunctionality emerges and is destroyed as the RC enters a chaotic regime that can lead to chaotic itinerancy.

math.DS↗

arXiv2023

Loxodromes in Open Multi-Section Lasers

We introduce a formalism to efficiently calculate lasing modes and optical power flow in multi-section lasers with open boundaries. The formalism is underpinned by a projection of the complex-valued electric field and its spatial derivative onto a suitably extended complex $\mathcal{Z}$-plane, to reduce the order of the problem and simplify analysis. In a single-section laser, we show that a laser mode is a loxodrome on the extended complex $\mathcal{Z}$-plane. In a multi-section laser, we obtain loxodromes for individual sections of the laser. Then, a multi-section mode is constructed by continuously concatenating individual loxodromes from each section using the open boundary conditions. A natural visualization of this construction is given by stereographic projection of the extended complex $\mathcal{Z}$-plane onto the Riemann sphere. Our formalism simplifies analysis of lasing modes in open multi-section lasers and provides new insight into the mode geometry and degeneracy.

physics.optics↗

arXiv2023

Transitional cluster dynamics in a model for delay-coupled chemical oscillators

Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in the experimental set-up controls the onset of oscillations via a Hopf bifurcation. For a smaller voltage, the oscillators exhibit simple, so-called primary, clustering patterns, where all phase differences between each set of coupled oscillators are identical. However, upon increasing the voltage, additional secondary states, where phase differences differ, are detected. Previous work on this system saw the development of a mathematical model that explains how the existence, stability, and common frequency of the experimentally observed cluster states can be accurately controlled by the delay time of the coupling. In this study, we revisit the mathematical model of the electrochemical oscillators to address open questions by means of bifurcation analysis. Our analysis reveals how the stable cluster states, corresponding to experimental observations, lose their stability via an assortment of bifurcation types. The analysis further reveals a complex interconnectedness between branches of different cluster types; in particular, we find that each secondary state provides a continuous transition between certain primary states. These connections are explained by studying the phase space and parameter symmetries of the respective states. Furthermore, we show that it is only for a larger value of the voltage parameter that the branches of secondary states develop intervals of stability. Otherwise, for a smaller voltage, all the branches of secondary states are completely unstable and therefore hidden to experimentalists.

math.DS↗

arXiv2022

Exploring the limits of multifunctionality across different reservoir computers

Multifunctional neural networks are capable of performing more than one task without changing any network connections. In this paper we explore the performance of a continuous-time, leaky-integrator, and next-generation `reservoir computer' (RC), when trained on tasks which test the limits of multifunctionality. In the first task we train each RC to reconstruct a coexistence of chaotic attractors from different dynamical systems. By moving the data describing these attractors closer together, we find that the extent to which each RC can reconstruct both attractors diminishes as they begin to overlap in state space. In order to provide a greater understanding of this inhibiting effect, in the second task we train each RC to reconstruct a coexistence of two circular orbits which differ only in the direction of rotation. We examine the critical effects that certain parameters can have in each RC to achieve multifunctionality in this extreme case of completely overlapping training data.

cs.LG↗

arXiv2021

Dynamics of targeted ransomware negotiation

In this paper, we consider how the development of targeted ransomware has affected the dynamics of ransomware negotiations to better understand how to respond to ransomware attacks. We construct a model of ransomware negotiations as an asymmetric non-cooperative two-player game. In particular, our model considers the investments that a malicious actor must make in order to conduct a successful targeted ransomware attack. We demonstrate how imperfect information is a crucial feature for replicating observed real-world behaviour. Furthermore, we present optimal strategies for both the malicious actor and the target, and demonstrate how imperfect information results in a non-trivial optimal strategy for the malicious actor.

math.DS↗

arXiv2020

Multifunctionality in a Reservoir Computer

Multifunctionality is a well observed phenomenological feature of biological neural networks and considered to be of fundamental importance to the survival of certain species over time. These multifunctional neural networks are capable of performing more than one task without changing any network connections. In this paper we investigate how this neurological idiosyncrasy can be achieved in an artificial setting with a modern machine learning paradigm known as `Reservoir Computing'. A training technique is designed to enable a Reservoir Computer to perform tasks of a multifunctional nature. We explore the critical effects that changes in certain parameters can have on the Reservoir Computers' ability to express multifunctionality. We also expose the existence of several `untrained attractors'; attractors which dwell within the prediction state space of the Reservoir Computer that were not part of the training. We conduct a bifurcation analysis of these untrained attractors and discuss the implications of our results.

cs.NE↗

arXiv2020

Border-collision bifurcations in a driven time-delay system

We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter space. The simplicity of our model enables us to study the dynamical features analytically. Specifically, these features are explained in terms of border-collision bifurcations of an associated Poincar\'e map. Given that time delay and periodic forcing are common ingredients in mathematical models, this analysis provides widely applicable insight.

nlin.CD↗

arXiv2017

The Devil is in the Details: Spectrum and Eigenvalue Distribution of the Discrete Preisach Memory Model

We consider the adjacency matrix associated with a graph that describes transitions between $2^{N}$ states of the discrete Preisach memory model. This matrix can also be associated with the last-in-first-out inventory management rule. We present an explicit solution for the spectrum by showing that the characteristic polynomial is the product of Chebyshev polynomials. The eigenvalue distribution (density of states) is explicitly calculated and is shown to approach a scaled Devil's staircase. The eigenvectors of the adjacency matrix are also expressed analytically.

math-ph↗

arXiv2016

Asymmetric pentagonal metal meshes for flexible transparent electrodes and heaters

Metal meshes have emerged as an important class of flexible transparent electrodes. We report on the characteristics of a new class of asymmetric meshes, tiled using a recently-discovered family of pentagons. Micron-scale meshes were fabricated on flexible polyethylene terephthalate substrates via optical lithography, metal evaporation (Ti 10 nm, Pt 50 nm) and lift-off. Three different designs were assessed, each with the same tessellation pattern and linewidth (5 micron), but with different sizes of the fundamental pentagonal unit. The designs corresponded to areal coverage of the metal patterns of 27% (Design#1), 14% (Design#2) and 9% (Design#3), respectively. Good mechanical stability was observed for both tensile strain and compressive strain. After 1,000 bending cycles, devices subjected to tensile strain showed fractional resistance increases in the range 8% to 17% with the lowest changes observed for Design#2. Devices subjected to compressive strain showed fractional resistance increases in the range 0% to 7% with best results observed for Design#1. The performance of the pentagonal metal mesh devices as visible transparent heaters via Joule heating was also assessed. A saturation temperature of 88 +/- 1 degrees C was achieved at low voltage (5 V) with a fast response time (~ 20 s) and a high thermal resistance (168 +/- 6 degrees C cm2/W). Finally, de-icing was successfully demonstrated (45 s at 5 V) for an ice layer on a glass coupon placed on top of the PET substrate.

cond-mat.mes-hall↗

arXiv2014

Multi-stabilities and symmetry-broken one-colour and two-colour states in closely coupled single-mode lasers

We theoretically investigate the dynamics of two mutually coupled identical single-mode semi-conductor lasers. For small separation and large coupling between the lasers, symmetry-broken one-colour states are shown to be stable. In this case the light output of the lasers have significantly different intensities while at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable symmetry-broken two-colour states, where both lasers lase simultaneously at two optical frequencies which are separated by up to 150~GHz. Using a five dimensional model we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-colour and two-colour states. Several of these states give rise to multi-stabilities and therefore allow for the design of all-optical memory elements on the basis of two coupled single-mode lasers. The switching performance of selected designs of optical memory elements is studied numerically.

nlin.CD↗

arXiv2013

An odd-number limitation of extended time-delayed feedback control in autonomous systems

We propose a necessary condition for the successful stabilisation of a periodic orbit using the extended version of time-delayed feedback control. This condition depends on the number of real Floquet multipliers larger than unity and is therefore related to the well-known odd-number limitation in non-autonomous systems. We show that the period of the orbit which is induced by mismatching the delay-time of the control scheme and the period of the uncontrolled orbit plays an important role in the formulation of the odd-number limitation in the autonomous case.

nlin.CD↗

arXiv2012

Bursting: when a cusp and a pitchfork interact

We present an experimental and theoretical study of an unusual bursting mechanism in a two-mode semiconductor laser with single-mode optical injection. By tuning the strength and frequency of the injected light we find a transition from purely single-mode intensity oscillations to bursting in the intensity of the uninjected mode. We explain this phenomenon on the basis of a simple two-dimensional dynamical system, and show that the bursting in our experiment is organised by a cusp-pitchfork bifurcation of limit cycles.

nlin.CD↗