arXiv subjects

S. John Hogan

Publications and source records attributed to S. John Hogan.

8 recordsLinked to original sources

arXiv2023

The effects of delay on the HKB model of human motor coordination

In this paper, we analyse the celebrated Haken-Kelso-Bunz (HKB) model, describing the dynamics of bimanual coordination, in the presence of delay. We study the linear dynamics, stability, nonlinear behaviour and bifurcations of this model by both theoretical and numerical analysis. We calculate in-phase and anti-phase limit cycles as well as quasi-periodic solutions via double Hopf bifurcation analysis and centre manifold reduction. Moreover, we uncover further details on the global dynamic behaviour by numerical continuation, including the occurrence of limit cycles in phase quadrature and 1-1 locking of quasi-periodic solutions.

math.DS↗

arXiv2023

Uncountably many cases of Filippov's sewed focus

The sewed focus is one of the singularities of planar piecewise smooth dynamical systems. Defined by Filippov in his book 'Differential Equations with Discontinuous Righthand Sides' (Kluwer, 1988), it consists of two invisible tangencies either side of the switching manifold. In the case of analytic focus-like behaviour, Filippov showed that the approach to the singularity is in infinite time. For the case of non-analytic focus-like behaviour, we show that the approach to the singularity can be in finite time. For the non-analytic sewed centre-focus, we show that there are uncountably many different topological types of local dynamics, including cases with infinitely many stable periodic orbits, and show how to create systems with periodic orbits intersecting any bounded symmetric closed set.

math.DS↗

arXiv2022

Modeling and SAR Imaging of the Sea Surface: a Review of the State-of-the-Art with Simulations

Among other remote sensing technologies, synthetic aperture radar (SAR) has become firmly established in the practice of oceanographic research. Despite solid experience in this field, comprehensive knowledge and interpretation of ocean/sea and vessel wave signatures on radar images are still very challenging. Many technical parameters and scanning conditions vary for different SAR platforms, which also imposes some restrictions on the cross-analysis of their respective images. Numerical simulation of SAR images allows the analysis of many radar imaging parameters including environmental, ship, or platform related. In this paper, we present a universal simulation framework for SAR imagery of the sea surface, which includes the superposition of sea-ship waves. This paper is the first attempt to cover exhaustively all SAR imaging effects for the sea waves and ship wakes scene. The study is based on well proven concepts: the linear theory of sea surface modeling, Michell thin-ship theory for Kelvin wake modeling, and ocean SAR imaging theory. We demonstrate the role of two main factors that affect imaging of both types of waves: (i) SAR parameters and (ii) Hydrodynamic related parameters such as wind state and Froude number. The SAR parameters include frequency, signal polarization, mean incidence angle, image resolution, variation by scanning platform (airborne or spaceborne) of the range-to-velocity (R/V) ratio, and velocity bunching with associated shifting, smearing and azimuthal cutoff effects. We perform modeling for five wave frequency spectra and four ship models. We also compare spectra in two aspects: with Cox and Munk's probability density function (PDF), and with a novel proposed evaluation of ship wake detectability. The simulation results agree well with SAR imaging theory. The study gives a fuller understanding of radar imaging mechanisms for sea waves and ship wakes.

physics.ao-ph↗

arXiv2021

Synchronization of networks of piecewise-smooth systems

We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were typically oriented toward guaranteeing global bounded synchronizability, local stability of the synchronization manifold, or achieving synchronization by exerting a control action on each node. Here we start by generalizing existing results on QUAD systems to the case of PWS systems, accounting for a large variety of nonlinear coupling laws. Then, we propose that a discontinuous coupling can be used to guarantee global synchronizability of a network of N PWS agents under mild assumptions on the individual dynamics. We provide extensive numerical simulations to gain insights on larger networks.

eess.SY↗

arXiv2021

The Geometry of the Painlevé paradox

Painlevé showed that there can be inconsistency and indeterminacy in solutions to the equations of motion of a 2D rigid body moving on a sufficiently rough surface. The study of Painlevé paradoxes in 3D has received far less attention. In this paper, we highlight the pivotal role in the dynamics of the azimuthal angular velocity Psi by proving the existence of three critical values of Psi, one of which occurs independently of any paradox. We show that the 2D problem is highly singular and uncover a rich geometry in the 3D problem which we use to explain recent numerical results.

math.DS↗

arXiv2019

Control of Painlevé Paradox in a Robotic System

The Painlevé paradox is a phenomenon that causes instability in mechanical systems subjects to unilateral constraints. While earlier studies were mostly focused on abstract theoretical settings, recent work confirmed the occurrence of the paradox in realistic set-ups. In this paper, we investigate the dynamics and presence of the Painlevé phenomenon in a twolinks robot in contact with a moving belt, through a bifurcation study. Then, we use the results of this analysis to inform the design of control strategies able to keep the robot sliding on the belt and avoid the onset of undesired lift-off. To this aim, through numerical simulations, we synthesise and compare a PID strategy and a hybrid force/motion control scheme, finding that the latter is able to guarantee better performance and avoid the onset of bouncing motion due to the Painlevé phenomenon.

eess.SY↗

arXiv2018

Resolution of the piecewise smooth visible-invisible two-fold singularity in $\mathbb{R}^3$ using regularization and blowup

Two-fold singularities in a piecewise smooth (PWS) dynamical system in $\mathbb{R}^3$ have long been the subject of intensive investigation. The interest stems from the fact that trajectories which enter the two-fold are associated with forward non-uniqueness. The key questions are: How do we continue orbits forward in time? Are there orbits that are distinguished among all the candidates? We address these questions by regularizing the PWS dynamical system for the case of the visible-invisible two-fold. Within this framework, we consider a regularization function outside the class of Sotomayor and Teixera. We then undertake a rigorous investigation, using geometric singular perturbation theory and blowup. We show that there is indeed a forward orbit $U$ that is distinguished amongst all the possible forward orbits leaving the two-fold. Working with a normal form of the visible-invisible two-fold, we show that attracting limit cycles can be obtained (due to the contraction towards $U$), upon composition with a global return mechanism. We provide some illustrative examples.

math.DS↗

arXiv2017

Contraction analysis of switched Filippov systems via regularization

We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that contrary to previous approaches, our conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.

eess.SY↗