Different Types Of Dynamics Research Articles

A mean field analysis of the role of indirect transmission in emergent infection events

We developed a mathematical model to investigate the role of indirect transmission in the spread of infectious diseases, using the illustrative example of sarcoptic mange as a case study. This disease can be transmitted through direct contact between an infected host and a susceptible one, or indirectly when potential hosts encounter infectious mites and larvae deposited in the environment, commonly referred to as fomites. Our focus is on exploring the potential of these infectious reservoirs as triggers for emerging infection events and as stable reservoirs of the disease. To achieve this, our mean field compartmental model incorporates the epidemiological dynamics driven by indirect transmission via fomites. We identify different types of dynamics that the system can go into, controlled by different levels of direct and indirect transmission. Among these, we find a new regime where the disease can emerge and persist over time solely through fomites, without the necessity for direct transmission. This possibility of the system reveals an evolutionary pathway that could enable the parasite to enhance its fitness beyond host co-evolution. We also define a new threshold based on an effective reproductive number, that enables us to predict the conditions for disease persistence. Our model allows us to assess the potential effectiveness of various disease intervention measures by incorporating a feature observed in real systems. We hope this contributes to a better understanding of infectious disease outbreaks.

Magnetoelectric fractals, Magnetoelectric parametric resonance and Hopf bifurcation

In the present work, we study the dynamics of the magnetic nanodisc coupled through a magnetoelectric coupling to a ferroelectric crystal. The model of our interest is nonlinear, and we explore the problem under different limits of weak and strong non-linearity. By applying two electric fields with different frequencies, we control the form of the confinement potential of a ferroelectric subsystem and realize different types of dynamics. We proved that the system is more sensitive to magnetoelectric coupling in the case of double-well potential. In particular, in the case of strong non-linearity, arbitrary small values of magnetoelectric coupling lead to chaotic dynamics. In essence, magnetoelectric coupling plays a role akin to the small perturbations destroying invariant tori according to the KAM theorem. We showed that bifurcations in the system are of Hopf’s type. We observed the formation of magnetoelectric fractals in the system. In the limit of weak non-linearity, we studied a problem of parametric nonlinear resonance and enhancement of magnetic oscillations through magnetoelectric coupling.

The level-crossing problem of a weakly damped particle in quadratic potential well under harmonic excitation

Escape and level-crossing are fundamental and closely related problems in transient dynamics. Often, when a particle reaches a critical displacement, its escape becomes inevitable. Therefore, escape models based on truncated potentials are often used, resulting in similar problems to level-crossing formulations. Two different types of dynamics can be identified, leading to different kinds of level-crossing depending on the relationship between the damping and the excitation level. The first one (“fast escape”) is mainly governed by the initial energy of the system, which is determined through the initial conditions. The second one (“slow escape”) is governed by the beatings determined through the relationship between external excitation and damping. An analytic approach for estimating the size and location of the safe basins (SBs) in the plane of the initial conditions (ICs) of a 1-DOF externally excited oscillator is suggested. It enables the identification of the set of ICs where the particle never reaches a certain threshold under the given excitation. The SBs depend on the damping coefficient and the excitation’s amplitude, frequency, and phase. Nonetheless, one can describe the essential properties of an SBs in the case of the almost resonant excitation using only two parameters: the forced response amplitude and the damping coefficient ratio to the difference between the natural and the excitation frequencies. Although the analysis is performed for a linear oscillator, it provides insight into the rush erosion process of the SBs (“Dover cliff” phenomenon), described previously only for nonlinear systems. The analysis reveals that the “Dover cliff” phenomenon is related to the decay rate of the transient motion and that it can occur even in linear systems too. From the engineering point of view, the rush erosion of the SBs is critical in noisy environments where devices operating in regions close to the “Dover cliff” are unsafe. Due to its simplicity, the proposed mechanical model might be generic for further analysis of the escape and level-crossing problems considering various nonlinearities (e.g., Coulomb friction, small polynomial-type nonlinearities of the restoring force, or constant restoring force). Possible applications include but are not limited to avoiding collisions for systems with clearances and durability analysis of brittle materials subjected to noisy loads.

Time-reversible dynamics in a system of two coupled active rotators

We study two coupled active rotators with Kuramoto-type coupling and focus our attention to specific transitional regimes where the coupling is neither attractive nor repulsive. We show that certain such situations at the edge of synchronization can be characterized by the existence of a time-reversal symmetry of the system. We identify two different cases with such a time-reversal symmetry. The first case is characterized by a non-reciprocal attractive/repulsive coupling. The second case is a reciprocal coupling exactly at the edge between attraction and repulsion. We give a detailed description of possible different types of dynamics and bifurcations for both cases. In particular, we show how the time-reversible coupling can induce both oscillation death and oscillation birth to the active rotators. Moreover, we analyse the coexistence of conservative and dissipative regions in phase space, which is a typical feature of systems with a time-reversal symmetry. We show also, how perturbations breaking the time-reversal symmetry and destroying the conservative regions can lead to complicated types of dissipative dynamics such as the emergence of long-period cycles showing a bursting-like behaviour.

Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions

The inhomogeneous population distribution appears as various population densities or different types of dynamics in distant sites of the extended habitat and may arise due to, for example, the resettlement features, the internal population structure, and the population dynamics synchronization mechanisms between adjacent subpopulations. In this paper, we propose the model of the spatio-temporal dynamics of two-age-structured populations coupled by migration (metapopulation) with long-range displacement. We study mechanisms leading to inhomogeneous spatial distribution as a type of cluster synchronization of population dynamics. To study the spatial patterns and synchronization, we use the method of constructing spatio-temporal profiles and spatial return maps. We found that patterns with spots or stripes are typical spatial structures with synchronous dynamics. In most cases, the spatio-temporal dynamics are mixed with randomly located single populations with strong burst (outbreak) of population size (solitary states). As the coupling parameters decrease, the number of solitary states grows, and they increasingly synchronize and form the clusters of solitary states. As a result, there are the several clusters with different dynamics. The appearance of these spatial patterns most likely occurs due to the multistability of the local age-structured population, leading to the spatio-temporal multistability.

Multi-scale description of pedestrian collective dynamics with port-Hamiltonian systems

<abstract><p>Port-Hamiltonian systems (PHS) theory is a recent but already well-established modelling approach for non-linear physical systems. Some studies have shown lately that PHS frameworks are relevant for modelling and control of swarm and multi-agent systems. We identify in this contribution a general class of microscopic force-based pedestrian models that can be formulated as a port-Hamiltonian system. The pedestrian PHS has linear structure and dissipation components. Non-linear effects come from isotropic pedestrian interactions. Simulation results on a torus with disordered initial states show that the port-Hamiltonian pedestrian model can exhibit different types of dynamics. They range from relaxed speed models with no interaction, dynamical billiards, or crystallization dynamics to realistic pedestrian collective behaviors, including lane and strip formation for counter and crossing flow. The port-Hamiltonian framework is a natural multiscale description of pedestrian dynamics as the Hamiltonian turns out to be a generic order parameter that allows us to identify specific behaviours of the dynamics from a macroscopic viewpoint. Particular cases even enable through energy balance to determine the Hamiltonian behavior without requiring the tedious computation of the microscopic dynamics. Using PHS theory, we systematically identify a critical threshold value for the Hamiltonian, which relies only on exogenous input and can be physically interpreted.</p></abstract>

Blood glucose kinetics during concentric and eccentric muscle contractions

Studies comparing the two classes of stimuli (concentric and eccentric) have shown differences in the improvement of cardiovascular, metabolic, and muscle strength gain. This is an experimental, quantitative, and prospective study that aimed to verify the effect of eccentric exercise on glycolytic consumption and kinetics. The blood glucose kinetics of 17 male subjects was evaluated during a treadmill exercise with a 10% declined floor and velocity that required a 60% metabolic activity of VO2max, for 30 minutes. Seventy-two hours later, the same subjects exercised on the treadmill with a 10% inclined floor and 60% VO2max, for 30 minutes. To quantify glucose, blood samples were collected before the exercise, every three minutes along the 30 minutes of physical activity, and five and 10 minutes after finishing the exercise. For the downward slope, there was a homogeneous group behavior for blood glucose dynamics during the exercise, which was characterized by a monotonic decrease of glucose levels until reaching a minimum value at experimental times between 20 and 30 min, followed by a progressive recovery toward initial values. For the acclivity condition, blood glucose dynamics did not follow such a homogeneous behavior. A set of different types of dynamics could be identified. Experimental data showed that the type of dynamics could be predicted, to some extent, by the basal blood glucose level of subjects. The type of floor slope (upward or downward) directly affected glycolytic consumption and kinetics for the individuals analyzed.

Frustration-driven Josephson phase dynamics

The Josephson equations predict remarkable effects concerning the phase state of a superconducting junction with an oscillating current induced by a static voltage. Whether the paradigm can be twisted by yielding an oscillating voltage without making use of harmonic drives is a fundamentally relevant problem yet not fully settled. Here, we demonstrate that a dynamical regime with an oscillating phase evolution is a general hallmark of driven Josephson systems exhibiting sign competition in the Josephson couplings. We show that in frustrated Josephson systems an oscillating phase dynamics gets switched on by driving the changeover among different ground states, which can be induced by varying the parameters that set the phase state. Remarkably, the character of the transitions in the Josephson phase space allows different types of dynamics, with few or several harmonics. This result sets out a characteristic mark of any superconducting system with frustrated Josephson couplings and can be exploited to disentangle the complexity of the underlying phases.

Complex dynamics and optimal control of monetary policy in a New Keynesian model with government debt

One of the central tasks of macroeconomic analysis is forecasting and control of economic agents’ expectations for key macroeconomic indicators such as inflation, gross domestic product (GDP), prices and others, etc., so that to achieve maximum level of their welfare through monetary and fiscal policy. This problem is solved within the framework of the optimal control theory using New Keynesian (NK) models that can demonstrate complex behavior, including periodic and chaotic dynamics, even in conditions of dynamical economic equilibrium. Revealing the economic mechanism for the emergence of such irregular dynamics can improve forecasting behavior of the model of the economy and stabilize undesirable dynamics. We consider this complex mechanism from two sides. First, we analyze how various monetary and fiscal policy regimes, active as well as passive, stimulate the emergence of different types of dynamics, both locally determinate and explosive ones, using the NK model with government debt as an example. Second, we clarify how government debt affects optimal monetary policy. A non-trivial backward integration algorithm is implemented to identify the initial state of the model, which leads to optimal dynamic equilibrium and the achievement of targeted values of key macroeconomic indicators.

Analysis of "big data" and mathematical modeling of the covid-19 epidemic in Europe

The regularities of the dynamics of the covid-19 pandemic in Ukraine and other European countries are studied by using the methods of analyzing "big data" in the form of time series and related information from open online sources. Statistical analysis of smoothed curves of new cases I (t), dead D (t), recovered R (t) and other time series has shown different types of dynamics: wave (i), quasi-wave with time shift (ii), stepwise (iii), with abnormally high or low amplitudes of local oscillations. The appropriate similarity trees have been constructed by using the nearest neighbor method. It is shown that the countries with different types of dynamics (i, ii, iii) are located in separate branches of the trees. The stability of zero and nonzero stationary points have been investigated on the basis of the popular mathematical model SIRS. The solutions of the linearized system have been obtained and the influence of the model parameters on the eigenvalues of the system matrix has been investigated. The presence of different types of dynamics is shown: with three negative real (a), one positive real (b), one real and a pair of complex conjugate(c) eigenvalues. The phase portraits have been constructed and the connection of the types of time series (i, ii, iii) and solutions (a, b, c) of the SIRS equations is shown. The obtained results allow us to estimate the dynamic behavior of the system, its stability or instability with the possibility of chaotic dynamics on the basis of the analysis of time series on any current day.

Network processes on clique-networks with high average degree: the limited effect of higher-order structure

In this paper, we investigate the effect of local structures on network processes. We investigate a random graph model that incorporates local clique structures, and thus deviates from the locally tree-like behavior of most standard random graph models. For the process of bond percolation, we derive analytical approximations for large percolation probabilities and the critical percolation value. Interestingly, these derivations show that when the average degree of a vertex is large, the influence of the deviations from the locally tree-like structure is small. In our simulations, this insensitivity to local clique structures often already kicks in for networks with average degrees as low as 6. Furthermore, we show that the different behavior of bond percolation on clustered networks compared to tree-like networks that was found in previous works can be almost completely attributed to differences in degree sequences rather than differences in clustering structures. We finally show that these results also extend to completely different types of dynamics, by deriving similar conclusions and simulations for the Kuramoto model on the same types of clustered and non-clustered networks.

Anatomical Model of Rat Ventricles to Study Cardiac Arrhythmias under Infarction Injury

Species-specific computer models of the heart are a novel powerful tool in studies of life-threatening cardiac arrhythmias. Here, we develop such a model aimed at studying infarction injury in a rat heart, the most common experimental system to investigate the effects of myocardial damage. We updated the Gattoni2016 cellular ionic model by fitting its parameters to experimental data using a population modeling approach. Using four selected cellular models, we studied 2D spiral wave dynamics and found that they include meandering and break-up. Then, using an anatomically realistic ventricular geometry and fiber orientation in the rat heart, we built a model with a post-infarction scar to study the electrophysiological effects of myocardial damage. A post-infarction scar was simulated as an inexcitable obstacle surrounded by a border zone with modified cardiomyocyte properties. For cellular models, we studied the rotation of scroll waves and found that, depending on the model, we can observe different types of dynamics: anchoring, self-termination or stable rotation of the scroll wave. The observed arrhythmia characteristics coincide with those measured in the experiment. The developed model can be used to study arrhythmia in rat hearts with myocardial damage from ischemia reperfusion and to examine the possible arrhythmogenic effects of various experimental interventions.

Description of turbulent dynamics in the interstellar medium: multifractal-microcanonical analysis

Observations of the interstellar medium (ISM) show a complex density and velocity structure, which is in part attributed to turbulence. Consequently, the multifractal formalism should be applied to observation maps of the ISM in order to characterize its turbulent and multiplicative cascade properties. However, the multifractal formalism, even in its more advanced and recent canonical versions, requires a large number of realizations of the system, which usually cannot be obtained in astronomy. We present a self-contained introduction to the multifractal formalism in a “microcanonical” version, which allows us, for the first time, to compute precise turbulence characteristic parameters from a single observational map without the need for averages in a grand ensemble of statistical observables (e.g., a temporal sequence of images). We compute the singularity exponents and the singularity spectrum for both observations and magnetohydrodynamic simulations, which include key parameters to describe turbulence in the ISM. For the observations we focus on the 250 μm Herschel map of the Musca filament. Scaling properties are investigated using spatial 2D structure functions, and we apply a two-point log-correlation magnitude analysis over various lines of the spatial observation, which is known to be directly related to the existence of a multiplicative cascade under precise conditions. It reveals a clear signature of a multiplicative cascade in Musca with an inertial range from 0.05–0.65 pc. We show that the proposed microcanonical approach provides singularity spectra that are truly scale invariant, as required to validate any method used to analyze multifractality. The obtained singularity spectrum of Musca, which is sufficiently precise for the first time, is clearly not as symmetric as usually observed in log-normal behavior. We claim that the singularity spectrum of the ISM toward Musca features a more log-Poisson shape. Since log-Poisson behavior is claimed to exist when dissipation is stronger for rare events in turbulent flows, in contrast to more homogeneous (in volume and time) dissipation events, we suggest that this deviation from log-normality could trace enhanced dissipation in rare events at small scales, which may explain, or is at least consistent with, the dominant filamentary structure in Musca. Moreover, we find that subregions in Musca tend to show different multifractal properties: While a few regions can be described by a log-normal model, other regions have singularity spectra better fitted by a log-Poisson model. This strongly suggests that different types of dynamics exist inside the Musca cloud. We note that this deviation from log-normality and these differences between subregions appear only after reducing noise features, using a sparse edge-aware algorithm, which have the tendency to “log-normalize” an observational map. Implications for the star formation process are discussed. Our study establishes fundamental tools that will be applied to other galactic clouds and simulations in forthcoming studies.

Neuronal-Plasticity and Reward-Propagation Improved Recurrent Spiking Neural Networks.

Different types of dynamics and plasticity principles found through natural neural networks have been well-applied on Spiking neural networks (SNNs) because of their biologically-plausible efficient and robust computations compared to their counterpart deep neural networks (DNNs). Here, we further propose a special Neuronal-plasticity and Reward-propagation improved Recurrent SNN (NRR-SNN). The historically-related adaptive threshold with two channels is highlighted as important neuronal plasticity for increasing the neuronal dynamics, and then global labels instead of errors are used as a reward for the paralleling gradient propagation. Besides, a recurrent loop with proper sparseness is designed for robust computation. Higher accuracy and stronger robust computation are achieved on two sequential datasets (i.e., TIDigits and TIMIT datasets), which to some extent, shows the power of the proposed NRR-SNN with biologically-plausible improvements.

Spatio-temporal dynamics in airport catchment areas: The case of the New York Multi Airport Region

Using the example of domestic connections departing from the New York Metropolitan Area, this paper contributes to research on airports' catchment areas in Multi Airport Regions by exploring their spatio-temporal dynamics. Given that previous research has consistently shown that airport accessibility and different elements of airport utility (fare, connectivity characteristics, on-time performance) are key drivers of airport choice, we draw the analogy with Huff models to calculate airport attractiveness to passengers in different census block groups. We marshal data sources that allow for an assessment of the spatio-temporal variability in the accessibility and utility of airports, which allows us to compare catchment areas for different times of the day, days of the week, and quarters of the year, and this for different utilities as well as overall utility. Results reveal different types of dynamics, and can be used as the input to follow-up research. We argue that such a model-based approach holds major potential in comparative research and research on MAR dynamics, but should be fine-tuned through the use of other information sources, refined model specifications, and state preference data.

Dynamics of a stochastic excitable system with slowly adapting feedback.

We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic bursting. We show how the system exhibits transitions between these dynamical regimes, as well as how one can enhance or suppress the coherence resonance or effectively control the features of the stochastic bursting. The setup can be considered a paradigmatic model for a neuron with a slow recovery variable or, more generally, as an excitable system under the influence of a nonlinear control mechanism. We employ a multiple timescale approach that combines the classical adiabatic elimination with averaging of rapid oscillations and stochastic averaging of noise-induced fluctuations by a corresponding stationary Fokker-Planck equation. This allows us to perform a numerical bifurcation analysis of a reduced slow system and to determine the parameter regions associated with different types of dynamics. In particular, we demonstrate the existence of a region of bistability, where the noise-induced switching between a stationary and an oscillatory regime gives rise to stochastic bursting.

Extracellular ionic fluxes suggest the basis for cellular life at the 1/f ridge of extended criticality

The criticality hypothesis states that a system may be poised in a critical state at the boundary between different types of dynamics. Previous studies have suggested that criticality has been evolutionarily selected, and examples have been found in cortical cell cultures and in the human nervous system. However, no one has yet reported a single- or multi-cell ensemble that was investigated ex vivo and found to be in the critical state. Here, the precise 1/f noise was found for pollen tube cells of optimum growth and for the physiological (“healthy”) state of blood cells. We show that the multi-scale processes that arise from the so-called critical phenomena can be a fundamental property of a living cell. Our results reveal that cell life is conducted at the border between order and disorder, and that the dynamics themselves drive a system towards a critical state. Moreover, a temperature-driven re-entrant state transition, manifest in the form of a Lorentz resonance, was found in the fluctuation amplitude of the extracellular ionic fluxes for the ensemble of elongating pollen tubes of Nicotiana tabacum L. or Hyacintus orientalis L. Since this system is fine-tuned for rapid expansion to reach the ovule at a critical temperature which results in fertilisation, the core nature of criticality (long-range coherence) offers an explanation for its potential in cell growth. We suggest that the autonomous organisation of expansive growth is accomplished by self-organised criticality, which is an orchestrated instability that occurs in an evolving cell.Graphic abstract

Dynamics of a predator-prey model with discrete and distributed delay

This paper considers a predator-prey model with discrete time delay representing prey handling time and assumed equal to the predator maturation period, and a distributed time delay describing intra-species interactions. We show that due to the delayed logistic growth of the prey, it is impossible for the species to become extinct through predation. Conditions for existence and local stability of the co-existence equilibrium are derived in terms of system parameters. Using techniques of centre manifold reduction and the normal form theory, we establish the direction of Hopf bifurcation of the co-existence equilibrium, as well as the stability of the bifurcating period solution. Numerical bifurcation analysis and simulations are performed to illustrate regions of stability of the co-existence equilibrium, to investigate how the amplitude and the period of bifurcating periodic solutions depend on parameters, and to demonstrate different types of dynamics of the system.

Cluster synchronization in networked nonidentical chaotic oscillators.

In exploring oscillator synchronization, a general observation is that as the oscillators become nonidentical, e.g., introducing parameter mismatch among the oscillators, the propensity for synchronization will be deteriorated. Yet in realistic systems, parameter mismatch is unavoidable and even worse in some circumstances, the oscillators might follow different types of dynamics. Considering the significance of synchronization to the functioning of many realistic systems, it is natural to ask the following question: Can synchronization be achieved in networked oscillators of clearly different parameters or dynamics? Here, by the model of networked chaotic oscillators, we are able to demonstrate and argue that, despite the presence of parameter mismatch (or different dynamics), stable synchronization can still be achieved on symmetric complex networks. Specifically, we find that when the oscillators are configured on the network in such a way that the symmetric nodes have similar parameters (or follow the same type of dynamics), cluster synchronization can be generated. The stabilities of the cluster synchronization states are analyzed by the method of symmetry-based stability analysis, with the theoretical predictions in good agreement with the numerical results. Our study sheds light on the interplay between symmetry and cluster synchronization in complex networks and give insights into the functionalities of realistic systems where nonidentical nonlinear oscillators are presented and cluster synchronization is crucial.

Dynamic Assessment of Construction Materials in Urban Building Stocks: A Critical Review.

There is a lack of understanding on the different types of dynamics of building stocks, in real life and in models. Moreover, there is now a particular interest in the embodied impacts of construction materials, since with the increasing efficiency of buildings operation, embodied impacts gain more importance in the overall building life cycle. This critical review wants to advance the understanding of the type of dynamics, methods, and tools used. The well-known IPAT equation is adapted for building stocks and three dynamics are defined: spatial, evolutionary temporal, and spatial-cohort dynamic. A framework is defined that can help researchers choose a method, tool, and dynamics of input parameters depending on their research goal, case study, and data. Moreover, generally valid conclusions are drawn, including MFA is useful to model spatially dynamic material flows; GIS is needed to include spatial dynamics. Retrofit, compared to construction and demolition, is understudied and usually analyzed through top-down methods. Material intensity and emission intensity are rarely modeled in a dynamic way. Overall, scholars seem to perform increasingly data intensive and complex studies tailored to a specific case study. However, there are big differences in the quality depending on the dynamic of input parameters.