EMERGING PROPERTIES IN POPULATION DYNAMICS WITH DIFFERENT TIME SCALES

1995 ◽  
Vol 03 (02) ◽  
pp. 591-602 ◽  
Author(s):  
PIERRE AUGER ◽  
JEAN-CHRISTOPHE POGGIALE
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Time Scale ◽  
Population Level ◽  
Nonlinear Process ◽  
Linear Process ◽  
Fast Time ◽  
Slow Part ◽  
Spatial Patches ◽  
Different Time Scales

The aim of this work is to show that at the population level, emerging properties may occur as a result of the coupling between the fast micro-dynamics and the slow macrodynamics. We studied a prey-predator system with different time scales in a heterogeneous environment. A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to the growth and the interactions between the species. Preys go on the spatial patches on which some resources are located and can be caught by the predators on them. The efficiency of the predators to catch preys is patch-dependent. Preys can be more easily caught on some spatial patches than others. Perturbation theory is used in order to aggregate the initial system of ordinary differential equations for the patch sub-populations into a macro-system of two differential equations governing the total populations. Firstly, we study the case of a linear process of migration for which the aggregated system is formally identical to the slow part of the full system. Then, we study an example of a nonlinear process of migration. We show that under these conditions emerging properties appear at the population level.

scholarly journals Buckling versus crystal expulsion controlled by deformation rate of particle-coated air bubbles in oil

2021 ◽  
Author(s):  
Saikat Saha ◽  
Francis Pagaud ◽  
Bernard P. Binks ◽  
Valeria Garbin
Keyword(s):  
Shelf Life ◽  
Time Scales ◽  
Time Scale ◽  
Deformation Rate ◽  
Interfacial Layer ◽  
Fast Time ◽  
Flow Conditions ◽  
The Stability ◽  
Different Time Scales ◽  
Processing Flow

Oil foams stabilized by crystallizing agents exhibit outstanding stability and show promise for applications in consumer products. The stability and mechanics imparted by the interfacial layer of crystals underpin product shelf-life, as well as optimal processing conditions and performance in applications. Shelf-life is affected by the stability against bubble dissolution over a long time scale, which leads to slow compression of the interfacial layer. In processing flow conditions, the imposed deformation is characterized by much shorter time scales. In practical situations, the crystal layer is therefore subjected to deformation on extremely different time scales. Despite its importance, our understanding of the behavior of such interfacial layers at different time scales remains limited. To address this gap, here we investigate the dynamics of single, crystal-coated bubbles isolated from an oleofoam, at two extreme timescales: the diffusion-limited timescale characteristic of bubble dissolution 10,000 s, and a fast time scale characteristic of processing flow conditions, 0.001 s. In our experiments, slow deformation is obtained by bubble dissolution, and fast deformation in controlled conditions with real-time imaging is obtained using ultrasound-induced bubble oscillations. The experiments reveal that the fate of the interfacial layer is dramatically affected by the dynamics of deformation: after complete bubble dissolution, a continuous solid layer remains; while after fast, oscillatory deformation of the layer, small crystals are expelled from the layer. This observation shows promise towards developing stimuli-responsive systems, with sensitivity to deformation rate, in addition to the already known thermo- and photo-responsiveness of oleofoams.

scholarly journals Li–Yorke Chaos in Hybrid Systems on a Time Scale

2015 ◽  
Vol 25 (14) ◽  
pp. 1540024 ◽  
Author(s):  
Marat Akhmet ◽  
Mehmet Onur Fen
Keyword(s):  
Differential Equations ◽  
Hybrid Systems ◽  
Time Scales ◽  
Time Scale ◽  
Impulsive Differential Equations ◽  
Reduction Technique ◽  
Duffing Equation ◽  
Dynamic Equations ◽  
Definition Of ◽  
First Time

By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li–Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.

scholarly journals Stationarity Testing of Accumulated Ethernet Traffic

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiping Lu ◽  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Time Scales ◽  
Unit Root ◽  
Time Scale ◽  
Unit Root Tests ◽  
Quantitative Results ◽  
Different Time Scales

We investigate the stationarity property of the accumulated Ethernet traffic series. We applied several widely used stationarity and unit root tests, such as Dickey-Fuller test and its augmented version, Phillips-Perron test, as well as the Kwiatkowski-Phillips-Schmidt-Shin test and some of its generalizations, to the assessment of the stationarity of the traffic traces at the different time scales. The quantitative results in this research provide evidence that when the time scale increases, the accumulated traffic series are more stationary.

scholarly journals Solvability and Stability of Impulsive Set Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Shihuang Hong ◽  
Jing Gao ◽  
Yingzi Peng
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Difference Equations ◽  
Time Scale ◽  
Dynamic Equations ◽  
Stability Of Solutions ◽  
Real Numbers ◽  
Generalized Derivative ◽  
Special Cases ◽  
Existence And Stability

A class of new nonlinear impulsive set dynamic equations is considered based on a new generalized derivative of set-valued functions developed on time scales in this paper. Some novel criteria are established for the existence and stability of solutions of such model. The approaches generalize and incorporate as special cases many known results for set (or fuzzy) differential equations and difference equations when the time scale is the set of the real numbers or the integers, respectively. Finally, some examples show the applicability of our results.

scholarly journals Multi-Time Scale Economic Optimization Dispatch of the Park Integrated Energy System

2021 ◽  
Vol 9 ◽  
Author(s):  
Peng Li ◽  
Fan Zhang ◽  
Xiyuan Ma ◽  
Senjing Yao ◽  
Zhuolin Zhong ◽  
...  
Keyword(s):  
Renewable Energy ◽  
Time Scales ◽  
Time Scale ◽  
Energy Systems ◽  
Energy System ◽  
Optimal Operation ◽  
Utilization Efficiency ◽  
Integrated Energy System ◽  
Operation Cost ◽  
Different Time Scales

The park integrated energy system (PIES) plays an important role in realizing sustainable energy development and carbon neutral. Furthermore, its optimization dispatch can improve the energy utilization efficiency and reduce energy systems operation cost. However, the randomness and volatility of renewable energy and the instability of load all bring challenges to its optimal operation. An optimal dispatch framework of PIES is proposed, which constructs the operation models under three different time scales, including day-ahead, intra-day and real-time. Demand response is also divided into three levels considering its response characteristics and cost composition under different time scales. The example analysis shows that the multi-time scale optimization dispatch model can not only meet the supply and demand balance of PIES, diminish the fluctuation of renewable energy and flatten load curves, but also reduce the operation cost and improve the reliability of energy systems.

scholarly journals Modelling of UV radiation variations at different time scales

2008 ◽  
Vol 26 (3) ◽  
pp. 441-446 ◽  
Author(s):  
J. L. Borkowski
Keyword(s):  
Uv Radiation ◽  
Time Scales ◽  
Time Scale ◽  
Global Radiation ◽  
Regression Method ◽  
Ozone Content ◽  
Explanatory Variables ◽  
Solar Uv ◽  
Solar Global Radiation ◽  
Different Time Scales

Abstract. Solar UV radiation variability in the period 1976–2006 is discussed with respect to the relative changes in the solar global radiation, ozone content, and cloudiness. All the variables were decomposed into separate components, representing variations of different time scales, using wavelet multi-resolution decomposition. The response of the UV radiation to the changes in the solar global radiation, ozone content, and cloudiness depends on the time scale, therefore, it seems reasonable to model separately the relation between UV and explanatory variables at different time scales. The wavelet components of the UV series are modelled and summed to obtain the fit of observed series. The results show that the coarser time scale components can be modelled with greater accuracy than fine scale components and the fitted values calculated by this method are in better agreement with observed values than values calculated by the regression method, in which variables were not decomposed. The residual standard error in the case of modelling with the use of wavelets is reduced by 14% in comparison to the regression method without decomposition.

Data-driven stochastic model for cross-interacting processes with different time scales

2021 ◽  
Author(s):  
Andrey Gavrilov ◽  
Aleksei Seleznev ◽  
Dmitry Mukhin ◽  
Alexander Feigin
Keyword(s):  
Time Series ◽  
Stochastic Model ◽  
Time Scales ◽  
Time Scale ◽  
Sampling Interval ◽  
Bayesian Optimization ◽  
Data Driven ◽  
Middle Pleistocene ◽  
Model Based ◽  
Different Time Scales

<p>The problem of modeling interaction between processes with different time scales is very important in geoscience. In this report, we propose a new form of empirical evolution operator model based on the analysis of multiple time series representing processes with different time scales. We assume that the time series are given on the same time interval.</p><p>To construct the model, we extend the previously developed general form of nonlinear stochastic model based on artificial neural networks and designed for the case of time series with constant sampling interval [1]. This sampling interval is related to the main time scale of the process under consideration, which is described by the deterministic component of the model, while the faster time scales are modeled by its stochastic component, possibly depending on the system’s state. This model also includes slower processes in the form of weak time-dependence, as well as external forcing. The structure of the model is optimized using Bayesian approach [1]. The model has proven its efficiency in a number of applications [2-4].</p><p>The idea of modeling time series with different time scales is to formulate the above-described model individually for each time scale, and then to include the parameterized influence of the other time scales in it. Particularly, the influence of “slower” time series is included in the form of parameter trends, and the influence of “faster” time series is included by time-averaging their statistics. The algorithm and first results of comparison between the new model and the model without cross-interactions will be discussed.</p><p>The work was supported by the Russian Science Foundation (Grant No. 20-62-46056).</p><p>1. Gavrilov, A., Loskutov, E., & Mukhin, D. (2017). Bayesian optimization of empirical model with state-dependent stochastic forcing. Chaos, Solitons & Fractals, 104, 327–337. http://doi.org/10.1016/j.chaos.2017.08.032</p><p>2. Mukhin, D., Kondrashov, D., Loskutov, E., Gavrilov, A., Feigin, A., & Ghil, M. (2015). Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models. Journal of Climate, 28(5), 1962–1976. http://doi.org/10.1175/JCLI-D-14-00240.1</p><p>3. Gavrilov, A., Seleznev, A., Mukhin, D., Loskutov, E., Feigin, A., & Kurths, J. (2019). Linear dynamical modes as new variables for data-driven ENSO forecast. Climate Dynamics, 52(3–4), 2199–2216. http://doi.org/10.1007/s00382-018-4255-7</p><p>4. Mukhin, D., Gavrilov, A., Loskutov, E., Kurths, J., & Feigin, A. (2019). Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition. Scientific Reports, 9(1), 7328. http://doi.org/10.1038/s41598-019-43867-3</p>

Problems with different time scales

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 101-139 ◽  
Author(s):  
Heinz-Otto Kreiss
Keyword(s):  
Time Scales ◽  
Complex Number ◽  
Initial Value Problem ◽  
Time Scale ◽  
Homogeneous Equation ◽  
Simple Problem ◽  
Initial Value ◽  
Small Constant ◽  
Image Position ◽  
Different Time Scales

In this section we discuss a very simple problem. Consider the scalar initial value problemHere ε > 0 is a small constant and a = a1 + ia2, a1, a2 real, is a complex number with |a| = 1. We can write down the solution of (1.1) explicity. It iswhereis the forced solution andis a solution of the homogeneous equationyS varies on the time scale ‘1’ while yF varies on the much faster scale 1/ε. We say that yS, yF vary on the slow and fast scale, respectively. We use also the phrase: yS and yF are the slow and the fast part of the solution, respectively.

Sign in / Sign up

Export Citation Format

Share Document