Noise-induced dynamical regimes in a system of globally coupled excitable units

2021 ◽  
Vol 31 (8) ◽  
pp. 083103
Author(s):  
V. V. Klinshov ◽  
S. Yu. Kirillov ◽  
V. I. Nekorkin ◽  
M. Wolfrum
Keyword(s):  
Dynamical Regimes

scholarly journals Effects of Vector Maturation Time on the Dynamics of Cassava Mosaic Disease

2021 ◽  
Vol 83 (8) ◽  
Author(s):  
F. Al Basir ◽  
Y. N. Kyrychko ◽  
K. B. Blyuss ◽  
S. Ray
Keyword(s):  
Time Delay ◽  
Plant Density ◽  
Plant Viruses ◽  
Mosaic Disease ◽  
Plant Diseases ◽  
Cassava Mosaic Disease ◽  
Maturation Time ◽  
Negative Effect ◽  
Dynamical Regimes

AbstractMany plant diseases are caused by plant viruses that are often transmitted to plants by vectors. For instance, the cassava mosaic disease, which is spread by whiteflies, has a significant negative effect on plant growth and development. Since only mature whiteflies can contribute to the spread of the cassava mosaic virus, and the maturation time is non-negligible compared to whitefly lifetime, it is important to consider the effects this maturation time can have on the dynamics. In this paper, we propose a mathematical model for dynamics of cassava mosaic disease that includes immature and mature vectors and explicitly includes a time delay representing vector maturation time. A special feature of our plant epidemic model is that vector recruitment is negatively related to the delayed ratio between vector density and plant density. We identify conditions of biological feasibility and stability of different steady states in terms of system parameters and the time delay. Numerical stability analyses and simulations are performed to explore the role of various parameters, and to illustrate the behaviour of the model in different dynamical regimes. We show that the maturation delay may stabilise epidemiological dynamics that would otherwise be cyclic.

TWOFOLD IMPACT OF DELAYED FEEDBACK ON COUPLED OSCILLATORS

2007 ◽  
Vol 17 (07) ◽  
pp. 2517-2530 ◽  
Author(s):  
OLEKSANDR V. POPOVYCH ◽  
VALERII KRACHKOVSKYI ◽  
PETER A. TASS
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Phase Synchronization ◽  
Threshold Value ◽  
Phase Oscillators ◽  
Intermediate Coupling ◽  
Rich Variety ◽  
Dynamical Regimes ◽  
The Impact

We present a detailed bifurcation analysis of desynchronization transitions in a system of two coupled phase oscillators with delay. The coupling between the oscillators combines a delayed self-feedback of each oscillator with an instantaneous mutual interaction. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. We show that an increase of the coupling strength between oscillators may lead to a loss of synchronization. Intriguingly, the delay has a twofold influence on the oscillations: synchronizing for small and intermediate coupling strength and desynchronizing if the coupling strength exceeds a certain threshold value. We show that the desynchronization transition has the form of a crisis bifurcation of a chaotic attractor of chaotic phase synchronization. This study contributes to a better understanding of the impact of time delay on interacting oscillators.

scholarly journals A simple molecular mechanism explains multiple patterns of cell-size regulation

2016 ◽  
Author(s):  
Morgan Delarue ◽  
Daniel Weissman ◽  
Oskar Hallatschek
Keyword(s):  
Cell Size ◽  
Critical Size ◽  
Size Control ◽  
Molecular Size ◽  
Massive Data ◽  
Initial Cell ◽  
Constant Size ◽  
Biophysical Mechanism ◽  
Dynamical Regimes ◽  
Shed Light

AbstractIncreasingly accurate and massive data have recently shed light on the fundamental question of how cells maintain a stable size trajectory as they progress through the cell cycle. Microbes seem to use strategies ranging from a pure sizer, where the end of a given phase is triggered when the cell reaches a critical size, to pure adder, where the cell adds a constant size during a phase. Yet the biological origins of the observed spectrum of behavior remain elusive. We analyze a molecular size-control mechanism, based on experimental data from the yeast S. cerevisiae, that gives rise to behaviors smoothly interpolating between adder and sizer. The size-control is obtained from the titration of a repressor protein by an activator protein that accumulates more rapidly with increasing cell size. Strikingly, the size-control is composed of two different regimes: for small initial cell size, the size-control is a sizer, whereas for larger initial cell size, is is an imperfect adder. Our model thus indicates that the adder and critical size behaviors may just be different dynamical regimes of a single simple biophysical mechanism.

scholarly journals Causal Discovery for Climate Time Series in the Presence of Unobserved Variables

2020 ◽  
Author(s):  
Andreas Gerhardus ◽  
Jakob Runge
Keyword(s):  
Time Series ◽  
Causal Discovery ◽  
Time Lags ◽  
Cause And Effect ◽  
Scientific Curiosity ◽  
Relevant Variables ◽  
Data Driven Approach ◽  
Dynamical Regimes ◽  
Unobserved Variables ◽  
Climate Time Series

<p>Scientific inquiry seeks to understand natural phenomena by understanding their underlying processes, i.e., by identifying cause and effect. In addition to mere scientific curiosity, an understanding of cause and effect relationships is necessary to predict the effect of changing dynamical regimes and for the attribution of extreme events to potential causes. It is thus an important question to ask how, in cases where controlled experiments are not feasible, causation can still be inferred from the statistical dependencies in observed time series.</p><p>A central obstacle for such an inference is the potential existence of unobserved causally relevant variables. Arguably, this is more likely to be the case than not, for example unmeasured deep oceanic variables in atmospheric processes. Unobserved variables can act as confounders (meaning they are a common cause of two or more observed variables) and thus introduce spurious, i.e., non-causal dependencies. Despite these complications, the last three decades have seen the development of so-called causal discovery algorithms (an example being FCI by Spirtes et al., 1999) that are often able to identify spurious associations and to distinguish them from genuine causation. This opens the possibility for a data-driven approach to infer cause and effect relationships among climate variables, thereby contributing to a better understanding of Earth's complex climate system.</p><p>These methods are, however, not yet well adapted to some specific challenges that climate time series often come with, e.g. strong autocorrelation, time lags and nonlinearities. To close this methodological gap, we generalize the ideas of the recent PCMCI causal discovery algorithm (Runge et al., 2019) to time series where unobserved causally relevant variables may exist (in contrast, PCMCI made the assumption of no confounding). Further, we present preliminary applications to modes of climate variability.</p>

scholarly journals A locally preferred structure characterises all dynamical regimes of a supercooled liquid

2016 ◽  
Vol 96 (12) ◽  
pp. 1212-1227 ◽  
Author(s):  
Ryan Soklaski ◽  
Vy Tran ◽  
Zohar Nussinov ◽  
K. F. Kelton ◽  
Li Yang
Keyword(s):  
Supercooled Liquid ◽  
Dynamical Regimes

INVESTIGATION OF THE INFLUENCE OF RANDOM PERTURBATIONS ON THE DYNAMICS OF THE SYSTEM IN THE SUSLOV PROBLEM

2021 ◽  
pp. 17-29
Author(s):  
E.A. Mikishanina ◽  
Keyword(s):  
Software Package ◽  
Strange Attractors ◽  
Phase Portraits ◽  
Deterministic System ◽  
Random Perturbations ◽  
Variable Parameters ◽  
Suslov Problem ◽  
Perturbed System ◽  
System A ◽  
Dynamical Regimes

The paper considers the generalized Suslov problem with variable parameters and the influence of random perturbations on the dynamics of the system under consideration. The physical meaning of the Suslov problem is Chaplygin's sleigh, which moves along the inner side of the circle. In the case of a deterministic system, a brief review of the previously obtained results is made, the presence of chaotic dynamics in the system and such effects as the appearance of a strange attractor and noncompact (escaping) trajectories is shown. Moreover, the latter may indicate a possible acceleration in the system. The appearance of chaotic strange attractors occurs due to a cascade of bifurcations of doubling the period. We also consider the dynamics of a perturbed system which arises due to the addition of «white noise» modeled by the Wiener process to one of the equations. Changes in the dynamics of a perturbed system compared to an unperturbed one are studied: chaotization of periodic regimes, the appearance of noncompact trajectories, and the premature destruction of strange attractors. In this paper, phase portraits, maps for the period, graphs of system solutions, and a chart of dynamical regimes are constructed using the Maple software package and the software package «Computer Dynamics: Chaos» (/http://site4.ics.org.ru//chaos_pack).

scholarly journals Dynamical Regimes of Giant Planet Polar Vortices [Icarus 1 (2019) 46-61]

Icarus ◽  
2020 ◽  
pp. 114065
Author(s):  
Shawn R. Brueshaber ◽  
Kunio M. Sayanagi ◽  
Timothy E. Dowling
Keyword(s):  
Giant Planet ◽  
Dynamical Regimes
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