Periodic trajectories for an age-structured prey–predator system with Michaelis–Menten functional response including delays and asymmetric diffusion

2021 ◽  
pp. 1-19
Author(s):  
PENG YANG ◽  
YUANSHI WANG
Keyword(s):  
Functional Response ◽  
Bifurcation Theory ◽  
Time Lag ◽  
Periodic Trajectories ◽  
Semilinear Equations ◽  
Dense Domain ◽  
Lag Effect ◽  
Age Structured ◽  
Densely Defined ◽  
Predator System

This paper studies the periodic trajectories of a novel age-structured prey–predator system with Michaelis–Menten functional response including delays and asymmetric diffusion. To begin with, the system is turned into an abstract non-densely defined Cauchy problem, and a time-lag effect in their interaction is investigated. Next, we acquire that this system appears a periodic orbit near the positive steady state by employing the method of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain, which is also the main result of this article. Finally, in order to illustrate our theoretical analysis more vividly, we make some numerical simulations and give some discussions.

Dynamics of one-prey two-predator system with square root functional response and time lag

2015 ◽  
Vol 08 (03) ◽  
pp. 1550029 ◽  
Author(s):  
O. P. Misra ◽  
Poonam Sinha ◽  
Chhatrapal Singh
Keyword(s):  
Numerical Simulation ◽  
Functional Response ◽  
Limit Cycles ◽  
Equilibrium Points ◽  
Time Lag ◽  
Critical Value ◽  
Square Root ◽  
Basic System ◽  
Functional Responses ◽  
Predator System

Animals grouping together is one of the most interesting phenomena in population dynamics and different functional responses as a result of prey–predator forming groups have been considered by many authors in their models. In the present paper we have considered a model for one prey and two competing predator populations with time lag and square root functional response on account of herd formation by prey. It is shown that due to the inclusion of another competing predator, the underlying system without delay becomes more stable and limit cycles do not occur naturally. However, after considering the effect of time lag in the basic system, limit cycles appear in the case of all equilibrium points when delay time crosses some critical value. From the numerical simulation, it is observed that the length of delay is minimum when only prey population survives and it is maximum when all the populations coexist.

scholarly journals Multiple Bifurcations and Chaos in a Discrete Prey-Predator System with Generalized Holling III Functional Response

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xia Liu ◽  
Yanwei Liu ◽  
Qiaoping Li
Keyword(s):  
Numerical Methods ◽  
Functional Response ◽  
Bifurcation Theory ◽  
Allee Effect ◽  
Center Manifold ◽  
Step Size ◽  
Center Manifold Theorem ◽  
Strong Allee Effect ◽  
Holling Iii Functional Response ◽  
Predator System

A prey-predator system with the strong Allee effect and generalized Holling type III functional response is presented and discretized. It is shown that the combined influences of Allee effect and step size have an important effect on the dynamics of the system. The existences of Flip and Neimark-Sacker bifurcations and strange attractors and chaotic bands are investigated by using the center manifold theorem and bifurcation theory and some numerical methods.

Stability in a Discrete Fractional Order Prey Predator System with Functional Response

2017 ◽  
Vol 7 (5) ◽  
pp. 630-633 ◽  
Author(s):  
A. George Maria Selvam ◽  
◽  
R. Janagaraj ◽  
Britto Jacob. S ◽  
◽  
...  
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Predator System

scholarly journals A Weighted-Time-Lag Method to Detect Lag Vegetation Response to Climate Variation: A Case Study in Loess Plateau, China, 1982–2013

2021 ◽  
Vol 13 (5) ◽  
pp. 923
Author(s):  
Qianqian Sun ◽  
Chao Liu ◽  
Tianyang Chen ◽  
Anbing Zhang
Keyword(s):  
Climate Change ◽  
Loess Plateau ◽  
Time Lag ◽  
New Method ◽  
Climate Factors ◽  
The Loess Plateau ◽  
Climate Conditions ◽  
Vegetation Growth ◽  
Lag Effect

Vegetation fluctuation is sensitive to climate change, and this response exhibits a time lag. Traditionally, scholars estimated this lag effect by considering the immediate prior lag (e.g., where vegetation in the current month is impacted by the climate in a certain prior month) or the lag accumulation (e.g., where vegetation in the current month is impacted by the last several months). The essence of these two methods is that vegetation growth is impacted by climate conditions in the prior period or several consecutive previous periods, which fails to consider the different impacts coming from each of those prior periods. Therefore, this study proposed a new approach, the weighted time-lag method, in detecting the lag effect of climate conditions coming from different prior periods. Essentially, the new method is a generalized extension of the lag-accumulation method. However, the new method detects how many prior periods need to be considered and, most importantly, the differentiated climate impact on vegetation growth in each of the determined prior periods. We tested the performance of the new method in the Loess Plateau by comparing various lag detection methods by using the linear model between the climate factors and the normalized difference vegetation index (NDVI). The case study confirmed four main findings: (1) the response of vegetation growth exhibits time lag to both precipitation and temperature; (2) there are apparent differences in the time lag effect detected by various methods, but the weighted time-lag method produced the highest determination coefficient (R2) in the linear model and provided the most specific lag pattern over the determined prior periods; (3) the vegetation growth is most sensitive to climate factors in the current month and the last month in the Loess Plateau but reflects a varied of responses to other prior months; and (4) the impact of temperature on vegetation growth is higher than that of precipitation. The new method provides a much more precise detection of the lag effect of climate change on vegetation growth and makes a smart decision about soil conservation and ecological restoration after severe climate events, such as long-lasting drought or flooding.

Information technology investment and innovation performance: does investment paradox exist?

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Peinan Ji ◽  
Xiangbin Yan ◽  
Yan Shi
Keyword(s):  
Information Technology ◽  
Time Lag ◽  
Innovation Performance ◽  
Test Model ◽  
It Investment ◽  
Firm Innovation ◽  
Data Set ◽  
Content Type ◽  
Lag Effect ◽  
Enterprise Innovation

Purpose The purpose of this study is to deepen the understanding of the effects of information technology (IT) investment on firm innovation performance and examining the investment paradox effect in China. Design/methodology/approach Using a sample of China’ public firms IT investment data between 2010 and 2016, the authors establish a test model of IT investment and innovation performance. Findings The result indicates that IT investment in firms have no effect on innovation performance in the investment period. However, in the full sample and manufacturing sample, the IT investment has a significant positive effect on innovation performance in the post-investment years. In addition, this study finds that large companies and low-age companies may contribute more to innovation when firm investment in IT. Research limitations/implications There are several limitations in this research. First, the authors are failed to obtain a larger sample about the IT investment information data set in China, so this study was compelled to use limited sample data from China, hence, this could lead to errors of too early generalization. Second, the authors use the number of invention patent applications to represent the performance of enterprise innovation, which may not show enterprise innovation effectively. Third, the firms in the sample are all in China Listed Companies, so this may not accurately reflect the entire environment of firm innovation performance, and could possibly. Practical implications The research confirms that there is a paradox and time lag effect in IT investment, which enterprises should pay attention to. Originality/value Existing research confirms that corporate IT investments can bring new products or services. However, the authors still do not know whether IT investment has improved the company’s ability of innovation. This study will fill this gap and the industry effect and time lag effect of the influence of IT investment on innovative performance are also examined.

scholarly journals Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and Cell-to-Cell Transmissions

2018 ◽  
Vol 28 (09) ◽  
pp. 1850109 ◽  
Author(s):  
Xiangming Zhang ◽  
Zhihua Liu
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Hiv Infection ◽  
Bifurcation Analysis ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Positive Equilibrium ◽  
Semilinear Equations ◽  
Age Structured ◽  
Hiv Infection Model

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD[Formula: see text] T cells by a logistic function and the infected CD[Formula: see text] T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a nontrivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out.

Numerical Investigations for the Effect of Slender Body on Dynamic Rolling Characteristics of a 80°/60° Double Delta Wing

2013 ◽  
Vol 444-445 ◽  
pp. 286-292
Author(s):  
Bing Han ◽  
Min Xu ◽  
Xi Pei ◽  
Xiao Min An
Keyword(s):  
Stokes Equations ◽  
Delta Wing ◽  
Time Lag ◽  
Slender Body ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Rolling Motion ◽  
Navier Stokes Equations ◽  
Lag Effect ◽  
Double Delta Wing

The effect of slender body on the rolling characteristics of a double delta wing is found by comparing the numerical simulation results of the double delta wing and wing-body configuration. The coupled computation system solving the Navier-Stokes equations and the rolling motion equation alternatively to obtain the unsteady vortical flow around the two configurations while rolling. The results conclusively showed the upwash effect of the slender body enhanced the energy of strake vortex and merged vortex.The aerodynamic lag of double delta wing is weak, contrarily, the time lag effect of the wing-body configuration is significant. The asymmetry vortices structure nearby the trailing edge are believed to be the main reason for the unsteady time lag effect.

scholarly journals An SEIR Model for Assessment of Current COVID-19 Pandemic Situation in the UK

2020 ◽  
Author(s):  
Peiliang Sun ◽  
Kang Li
Keyword(s):  
Seasonal Influenza ◽  
Time Lag ◽  
Seir Model ◽  
Infected People ◽  
Proposed Model ◽  
Lag Effect ◽  
Novel Coronavirus ◽  
The Uk ◽  
Specific Symptoms ◽  
Limited Testing

AbstractThe ongoing COVID-19 pandemic spread to the UK in early 2020 with the first few cases being identified in late January. A rapid increase in confirmed cases started in March, and the number of infected people is however unknown, largely due to the rather limited testing scale. A number of reports published so far reveal that the COVID-19 has long incubation period, high fatality ratio and non-specific symptoms, making this novel coronavirus far different from common seasonal influenza. In this note, we present a modified SEIR model which takes into account the time lag effect and probability distribution of model states. Based on the proposed model, it is estimated that the actual total number of infected people by 1 April in the UK might have already exceeded 610,000. Average fatality rates under different assumptions at the beginning of April 2020 are also estimated. Our model also reveals that the R0 value is between 7.5–9 which is much larger than most of the previously reported values. The proposed model has a potential to be used for assessing future epidemic situations under different intervention strategies.

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