scholarly journals Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal Intra-Specific Competition for Both the Prey Species

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 101 ◽  
Author(s):  
Kalyan Manna ◽  
Vitaly Volpert ◽  
Malay Banerjee
Keyword(s):  
Prey Species ◽  
Population Distribution ◽  
Chaotic Oscillation ◽  
Turing Instability ◽  
Transient Dynamics ◽  
Nonlocal Interaction ◽  
Interaction Terms ◽  
Population Distributions ◽  
Predator Model ◽  
Spatiotemporal Models

Investigation of interacting populations is an active area of research, and various modeling approaches have been adopted to describe their dynamics. Mathematical models of such interactions using differential equations are capable to mimic the stationary and oscillating (regular or irregular) population distributions. Recently, some researchers have paid their attention to explain the consequences of transient dynamics of population density (especially the long transients) and able to capture such behaviors with simple models. Existence of multiple stationary patches and settlement to a stable distribution after a long quasi-stable transient dynamics can be explained by spatiotemporal models with nonlocal interaction terms. However, the studies of such interesting phenomena for three interacting species are not abundant in literature. Motivated by these facts here we have considered a three species prey–predator model where the predator is generalist in nature as it survives on two prey species. Nonlocalities are introduced in the intra-specific competition terms for the two prey species in order to model the accessibility of nearby resources. Using linear analysis, we have derived the Turing instability conditions for both the spatiotemporal models with and without nonlocal interactions. Validation of such conditions indicates the possibility of existence of stationary spatially heterogeneous distributions for all the three species. Existence of long transient dynamics has been presented under certain parametric domain. Exhaustive numerical simulations reveal various scenarios of stabilization of population distribution due to the presence of nonlocal intra-specific competition for the two prey species. Chaotic oscillation exhibited by the temporal model is significantly suppressed when the populations are allowed to move over their habitat and prey species can access the nearby resources.

scholarly journals Research on Human Travel Correlation for Urban Transport Planning Based on Multisource Data

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 195
Author(s):  
Hua Chen ◽  
Ming Cai ◽  
Chen Xiong
Keyword(s):  
Travel Demand ◽  
Population Distribution ◽  
Human Mobility ◽  
Urban Transport ◽  
License Plate ◽  
Traffic Patterns ◽  
Trajectory Data ◽  
Transport Planning ◽  
Population Distributions ◽  
Single Dataset

With the rapid development of positioning techniques, a large amount of human travel trajectory data is collected. These datasets have become an effective data resource for obtaining urban traffic patterns. However, many traffic analyses are only based on a single dataset. It is difficult to determine whether a single-dataset-based result can meet the requirement of urban transport planning. In response to this problem, we attempted to obtain traffic patterns and population distributions from the perspective of multisource traffic data using license plate recognition (LPR) data and cellular signaling (CS) data. Based on the two kinds of datasets, identification methods of residents’ travel stay point are proposed. For LPR data, it was identified based on different vehicle speed thresholds at different times. For CS data, a spatiotemporal clustering algorithm based on time allocation was proposed to recognize it. We then used the correlation coefficient r and the significance test p-values to analyze the correlations between the CS and LPR data in terms of the population distribution and traffic patterns. We studied two real-world datasets from five working days of human mobility data and found that they were significantly correlated for the stay and move population distributions. Then, the analysis scale was refined to hour level. We also found that they still maintain a significant correlation. Finally, the origin–destination (OD) matrices between traffic analysis zones (TAZs) were obtained. Except for a few TAZs with poor correlations due to the fewer LPR records, the correlations of the other TAZs remained high. It showed that the population distribution and traffic patterns computed by the two datasets were fairly similar. Our research provides a method to improve the analysis of complex travel patterns and behaviors and provides opportunities for travel demand modeling and urban transport planning. The findings can also help decision-makers understand urban human mobility and can serve as a guide for urban management and transport planning.

scholarly journals Ecological and evolutionary dynamics of interconnectedness and modularity

2018 ◽  
Vol 115 (4) ◽  
pp. 750-755 ◽  
Author(s):  
Jan M. Nordbotten ◽  
Simon A. Levin ◽  
Eörs Szathmáry ◽  
Nils C. Stenseth
Keyword(s):  
Population Dynamics ◽  
Natural Selection ◽  
Evolution Equation ◽  
Evolutionary Dynamics ◽  
Population Distribution ◽  
Theoretical Framework ◽  
Ecological System ◽  
Macro Level ◽  
Population Distributions ◽  
Trait Space

In this contribution, we develop a theoretical framework for linking microprocesses (i.e., population dynamics and evolution through natural selection) with macrophenomena (such as interconnectedness and modularity within an ecological system). This is achieved by developing a measure of interconnectedness for population distributions defined on a trait space (generalizing the notion of modularity on graphs), in combination with an evolution equation for the population distribution. With this contribution, we provide a platform for understanding under what environmental, ecological, and evolutionary conditions ecosystems evolve toward being more or less modular. A major contribution of this work is that we are able to decompose the overall driver of changes at the macro level (such as interconnectedness) into three components: (i) ecologically driven change, (ii) evolutionarily driven change, and (iii) environmentally driven change.

A PREY-PREDATOR MODEL WITH DIFFUSION AND A SUPPLEMENTARY RESOURCE FOR THE PREY IN A TWO‐PATCH ENVIRONMENT

2005 ◽  
Vol 9 (1) ◽  
pp. 9-24 ◽  
Author(s):  
J. Dhar
Keyword(s):  
Steady State ◽  
Asymptotic Stability ◽  
Prey Species ◽  
Steady State Solution ◽  
State Solution ◽  
Prey Population ◽  
Predator Species ◽  
Additional Resource ◽  
Linear And Nonlinear ◽  
Predator Model

In this paper, a prey‐predator dynamics, where the predator species partially depends upon the prey species, in a two patch habitat with diffusion and there is a non‐diffusing additional resource for the prey population, is modeled and analyzed. It is shown, that there exists a positive, monotonic, continuous steady state solution with continuous matching at the interface for both the species separately. Further, we obtain conditions for asymptotic stability for both linear and nonlinear cases. Šiame straipsnyje modeliuojama ir analizuojama plešr‐unu ir auku dinamika, laikant, kad plešr-unu populiacija dalinai priklauso nuo auku skačiaus. Areala sudaro dvi sritys, kuriose vyksta populiaciju individu difuzija, be to, aukoms yra išskirtas nedifunduojantis resursas. Irodyta, kad egzistuoja teigiamas, monotoniškas, tolydus stacionarusis sprendinys, tenkinantis tolydumo salyga abiems populiacijoms atskirai. Gautos asimptotinio stabilumo salygos tiesiniu ir netiesiniu atvejais.

scholarly journals Estimation of population distributions of habitual nutrient intakebased on a short-run weighed food diary

2000 ◽  
Vol 83 (3) ◽  
pp. 287-293 ◽  
Author(s):  
Clifton Gay
Keyword(s):  
Nutrient Intake ◽  
Population Distribution ◽  
Random Component ◽  
Food Diary ◽  
Nutrient Intakes ◽  
Diary Data ◽  
Population Distributions ◽  
Short Run ◽  
Nationally Representative

There have been many attempts to characterize day-to-day variation in nutrient intake. This variation has a fixed component, associated with particular days of the week, and a random component. Both components were studied for a range of nutrients, using 4 d weighed diary data from a large, nationally representative survey of people aged 65 years or over. Since day-to-day variation may distort the characterization of the population distribution of habitual nutrient intakes, especially when diets are studied over only a small number of days, a statistical method was developed to correct for this distortion. Results suggested that population distributions of habitual nutrient intake could be accurately constructed from 4 d weighed diary data and that the method might be successfully applied to studies based on as little as 2 d of observation. The method is particularly valuable for correcting estimates of extreme nutrient intakes for biases induced by uneven representation of days of the week and by within-person variation.

scholarly journals Estimating Hilly Areas Population Using a Dasymetric Mapping Approach: A Case of Sri Lanka’s Highest Mountain Range

2019 ◽  
Vol 8 (4) ◽  
pp. 166 ◽  
Author(s):  
Ananda Karunarathne ◽  
Gunhak Lee
Keyword(s):  
Land Use ◽  
Population Distribution ◽  
Estimation Methods ◽  
Mountain Range ◽  
Dasymetric Mapping ◽  
Ancillary Data ◽  
Hilly Area ◽  
Fine Grain ◽  
Population Distributions ◽  
Gis Environment

Since populations in the developing world have been rapidly increasing, accurately determining the population distribution is becoming more critical for many countries. One of the most widely used population density estimation methods is dasymetric mapping. This can be defined as a precise method for areal interpolation between different spatial units. In most applications of dasymetric mapping, land use and land cover data have been considered as ancillary data for the areal disaggregation process. This research presents an alternative dasymetric approach using area specific ancillary data for hilly area population mapping in a GIS environment. Specifically, we propose a Hilly Area Dasymetric Mapping (HDM) technique by combining topographic variables and land use to better disaggregate hilly area population distribution at fine-grain division of ancillary units. Empirical results for Sri Lanka’s highest mountain range show that the combined dasymetric approach estimates hilly area population most accurately and because of the significant association that is found to exist between topographic variables and population distribution within this setting. This research is expected to have significant implications for national and regional planning by providing useful information about actual population distributions in environmentally hazardous and sparsely populated areas.

DYNAMICAL STUDY OF DISCRETE-TIME PREY–PREDATOR MODEL WITH CONSTANT PREY REFUGE UNDER IMPRECISE BIOLOGICAL PARAMETERS

2020 ◽  
Vol 28 (03) ◽  
pp. 681-699
Author(s):  
P. K. SANTRA ◽  
G. S. MAHAPATRA
Keyword(s):  
Discrete Time ◽  
Discrete Model ◽  
Prey Species ◽  
Complex Nature ◽  
Biological Parameters ◽  
Constant Number ◽  
Prey Refuge ◽  
Dynamical Study ◽  
Dynamical Properties ◽  
Predator Model

The objective of this paper is to study the dynamical properties of a discrete-time prey–predator model under imprecise biological parameters. We consider refuge for prey species as a constant number. The equilibria of the model are obtained, and the dynamic behaviors of the proposed system are examined for the interval biological parameters. Simulations of the model are performed for different parameters of the model. Numerical simulations demonstrate that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.

scholarly journals DETERMINISTIC CHAOS VERSUS STOCHASTIC OSCILLATION IN A PREY-PREDATOR-TOP PREDATOR MODEL

2011 ◽  
Vol 16 (3) ◽  
pp. 343-364 ◽  
Author(s):  
Ranjit Kumar Upadhyay ◽  
Malay Banerjee ◽  
Rana Parshad ◽  
Sharada Nandan Raw
Keyword(s):  
Deterministic Model ◽  
Driving Forces ◽  
Equilibrium Points ◽  
Chaotic Oscillation ◽  
Three Dimensional ◽  
Deterministic Chaos ◽  
Model System ◽  
Dynamical Analysis ◽  
Interior Equilibrium ◽  
Predator Model

The main objective of the present paper is to consider the dynamical analysis of a three dimensional prey-predator model within deterministic environment and the influence of environmental driving forces on the dynamics of the model system. For the deterministic model we have obtained the local asymptotic stability criteria of various equilibrium points and derived the condition for the existence of small amplitude periodic solution bifurcating from interior equilibrium point through Hopf bifurcation. We have obtained the parametric domain within which the model system exhibit chaotic oscillation and determined the route to chaos. Finally, we have shown that chaotic oscillation disappears in presence of environmental driving forces which actually affect the deterministic growth rates. These driving forces are unable to drive the system from a regime of deterministic chaos towards a stochastically stable situation. The stochastic stability results are discussed in terms of the stability of first and second order moments. Exhaustive numerical simulations are carried out to validate the analytical findings.

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