Dynamics Of Spatiotemporal Patterns Research Articles

The impact of vaccination strategy on the spatiotemporal pattern dynamics of a COVID-19 epidemic model

The impact of vaccination strategy on the spatiotemporal pattern dynamics of a COVID-19 epidemic model

Detecting Changes in the Spatiotemporal Pattern of Bike Sharing: A Change-Point Topic Model

Detecting latent changes in the spatiotemporal pattern of bike sharing is critical to recognizing the impacts of various exogenous factors and significant events. Although extensive studies have investigated the spatiotemporal pattern dynamics in transportation systems, research that explicitly models the changing regularity and captures its latent changes is very scarce. To fill this research gap, we develop a change-point topic model that incorporates multinomial logit models into multi-dimensional latent Dirichlet allocation to decompose the spatiotemporal pattern into a mixture of activity patterns; meanwhile, our model captures the changing regularity of activity prevalence and its latent changes by integrating Dirichlet multinomial regression and hidden Markov models. We estimate the parameters of our model based on collapsed Gibbs sampling. We conduct numerical experiments using publicly available bike sharing trip records collected in New York. Results show that our model successfully distinguishes several meaningful activity categories, such as commuting. Furthermore, the detected pattern changes offer several insights into the impacts of associated events. Our model also improves the goodness of fit and predictive performance for the spatiotemporal attributes of trips.

Alteration in Cross Diffusivities Governs the Nature and Dynamics of Spatiotemporal Pattern Formation.

Realizing spatiotemporal patterns out of a chemical reaction diffusion system remains an experimental challenge owing to the difficulty in overcoming the stringent condition of diffusion driven instability. Herein, by considering the spatially extended Gray-Scott model system, we have investigated how the cross diffusivities of the reactants involved influence the nature and dynamics of spatiotemporal patterns. Our study unravels that in absence of diffusion driven instability, spatially inhomogeneous patterns can be obtained for the Gray-Scott model system, and unstable time dependent patterns can be stabilized just by adjusting cross diffusivities of the reactants. Interestingly, the effect of cross diffusion in presence of the diffusion driven instability can differentially alter the speed of pattern formation, and potentially modify the nature of the spatiotemporal patterns obtained under different parametric conditions. Experimental verification of our findings may allow us to observe spatiotemporal patterns beyond the regime of classical Turing instability.

Role of Thermal Noise in Dynamics of Non-equilibrium Systems: Macro-, Meso- and Microscopic

In this short review we discuss a decisive and some time unexpected role of a thermal noise in spatio-temporal dynamics of three different non-equilibrium systems, distinguished by their spatial scales, namely macroscopic, mesoscopic as well as microscopic, and by corresponding physical parameters relevant to their susceptibility to thermal fluctuations. As examples of such non-equilibrium systems, we choose a spatio-temporal pattern dynamics in a Rayleigh–Benard convection of a fluid in the vicinity of the gas-liquid critical point, as a macroscopic system; a spatio-temporal dynamics of a vesicle in shear as well as linear flows, as a mesoscopic system; and a dynamics of long flexible linear polymer molecules in a shear flow, as a microscopic system.

Effect of electromagnetic radiation on the dynamics of spatiotemporal patterns in memristor-based neuronal network

Modulational instability, as a mechanism of wave trains and soliton formation in biological system, is explored in the frame work of the new FitzHugh–Nagumo model. This model considered chain networks with memristive synaptic connection between adjacent neurons. This connection replaces the synaptic coupling and neurons bridged for signal exchange. From the physical law of electromagnetic induction, we interpret the traditional current term as magnetic flux variable. Magnetic flux is used to describe time-varying electromagnetic field setup in cells as a result of internal bioelectricity of the nervous system as well as when cells are exposed to external electromagnetic field. We reduced the whole network dynamical equations through multi-scale expansion to obtain a single differential–difference nonlinear equation of Schrodinger type. Linear stability is then performed with emphasis on memristive synaptic coupling. The conditions under which uniform plane waves propagating in the network become stable or unstable under small perturbation are calculated and plotted. Numerical experiments confirm our analytical predictions as the network supports localized mode excitations, spike-like, identified as quasi-periodic patterns, with some features of synchronization. It is confirmed that under strong electromagnetic radiation, the propagating waves encountered turbulent electrical activities, with patterns breakdown into a homogeneous state. This disordered state, collapse and instability of traveling pulse are monitored and analyzed using the sampled time series for membrane potential. It decreases to quiescent state under strong electromagnetic field. This could provide some guidance to understanding some neurodegenerative manifestations linked with high radiation exposure.

Synchronization and control in time-delayed complex networks and spatio-temporal patterns

This special topics issue is a collection of contributions on the recent developments of control and synchronization in time delayed systems and space time chaos. The various articles report interesting results on time delayed complex networks; fractional order delayed models; dynamics of spatio-temporal patterns; stochastic models etc. Experimental analysis on synchronization, dynamics and control of chaos are also well investigated using Field Programmable Gate Array (FPGA), circuit realizations and chemical reactions.

Survival benefits in mimicry: A quantitative framework

Mimicry is a resemblance between species that benefits at least one of the species. It is a ubiquitous evolutionary phenomenon particularly common among prey species, in which case the advantage involves better protection from predation. We formulate a mathematical description of predation, to investigate benefits and disadvantages of mimicry. The basic setup involves differential equations for quantities representing predator behavior, namely, the probabilities for attacking prey at the next encounter. Using this framework, we present new quantitative results, and also provide a unified description of a significant fraction of the quantitative mimicry literature. The new results include “temporary” mutualism between prey species, and an optimal density at which the survival benefit is greatest for the mimic. The formalism leads naturally to extensions in several directions, such as the interplay of mimicry with population dynamics, studies of spatiotemporal patterns, etc. We demonstrate this extensibility by presenting some explorations on spatiotemporal pattern dynamics.

Resonantly forced inhomogeneous reaction-diffusion systems.

The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex Ginzburg-Landau equation in the 3:1 resonance regime. Front roughening and spontaneous nucleation of target patterns are observed and characterized. Time dependent spatially varying forcing fields are studied in the 3:1 forced FitzHugh-Nagumo system. The periodic variation of the spatially random forcing amplitude breaks the symmetry among the three quasi-homogeneous states of the system, making the three types of fronts separating phases inequivalent. The resulting inequality in the front velocities leads to the formation of "compound fronts" with velocities lying between those of the individual component fronts, and "pulses" which are analogous structures arising from the combination of three fronts. Spiral wave dynamics is studied in systems with compound fronts. (c) 2000 American Institute of Physics.

Dynamics of spatio-temporal patterns in associative networks of spiking neurons

This paper studies dynamical properties of spatio-temporal pattern sequences (‘synfire chains’) in associative networks of spiking neurons. Employing postsynaptic potentials with a finite rise time, the replay speed of stored sequences can be controled by unspecific background signals. In addition, the speed also depends on the number of co-activated sequences, but balanced inhibition can prevent this dependency. An implicit equation is derived and solved numerically which relates the speed to the network parameters. Simulations reveal instabilities for low and high control signals, which are traced back to four different destabilizing mechanisms.

Spatially resolved infrared spectroscopy: a novel technique for in situ study of spatial surface coverage during CO oxidation on supported catalysts

A spatially resolved infrared (IR) imaging technique to monitor the linear adsorbed CO coverage on supported catalyst surface combining an IR bandpass filter and an IR thermography camera has been developed. Images acquired during the CO adsorption/desorption and ignition indicate that the technique provides an excellent method to image the change of surface coverage with a spatial resolution. It is expected that the combination of infrared thermography with spatially resolved imaging of surface coverage will provide a deeper insight in the dynamics of spatio-temporal patterns on heterogeneous catalysts.

Complex spatiotemporal dynamics of current filaments in crossed electric and magnetic fields.

We propose a novel model for the nonlinear dynamics of spatiotemporal patterns in semiconductors with negative differential conductivity under the influence of a transverse magnetic field. Dielectric relaxation of both the applied electric field and the Hall field combined with the generation-recombination kinetics of the carriers obtained from a Monte Carlo simulation induces a transverse motion of the current filaments and complex sequences of nucleation, traveling, and destruction of filaments which result in chaotic current and voltage oscillations.