scholarly journals Stability and bifurcation in a two-patch model with additive Allee effect

2021 ◽  
Vol 7 (1) ◽  
pp. 536-551
Author(s):  
Lijuan Chen ◽  
◽  
Tingting Liu ◽  
Fengde Chen
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Population Density ◽  
Mathematical Analysis ◽  
Allee Effect ◽  
Total Population ◽  
Population Abundance ◽  
Dispersal Rate ◽  
Saddle Node Bifurcation ◽  
Patch Model

<abstract><p>A two-patch model with additive Allee effect is proposed and studied in this paper. Our objective is to investigate how dispersal and additive Allee effect have an impact on the above model's dynamical behaviours. We discuss the local and global asymptotic stability of equilibria and the existence of the saddle-node bifurcation. Complete qualitative analysis on the model demonstrates that dispersal and Allee effect may lead to persistence or extinction in both patches. Also, combining mathematical analysis with numerical simulation, we verify that the total population abundance will increase when the Allee effect constant $ a $ increases or $ m $ decreases. And the total population density increases when the dispersal rate $ D_{1} $ increases or the dispersal rate $ D_{2} $ decreases.</p></abstract>

Effects of phytoseiid predators on the sex ratio of the spider mite Panonychus ulmi

1991 ◽  
Vol 69 (1) ◽  
pp. 208-212 ◽  
Author(s):  
Dan L. Johnson ◽  
Heather C. Proctor
Keyword(s):  
Population Density ◽  
Sex Ratio ◽  
Spider Mite ◽  
Total Population ◽  
Panonychus Ulmi ◽  
Encounter Rate ◽  
Male Mortality ◽  
Adult Sex Ratio ◽  
Biased Sex Ratio ◽  
Male Activity

The effect of predator presence on the adult sex ratio of a spider mite (Panonychus ulmi) was examined in a field experiment. Phytoseiid predators (chiefly Typhlodromus occidentalis) were removed from 32 trees harboring P. ulmi populations, and allowed to remain at natural levels on 32 other trees. Both total population density and proportion of males in the prey population were significantly higher in predator-free trees. Mechanisms that could explain the increase in the proportion of males are examined. The most probable is that greater male activity results in a higher encounter rate between predator and prey, and that subsequent higher male mortality when predators are present exaggerates the female-biased sex ratio. The theoretical effects of sex-biased predation on diplo-diploid and haplo-diploid organisms are discussed.

scholarly journals Mathematical Analysis of an Immune-structured Hikungunya Transmission Model

2019 ◽  
Vol 12 (4) ◽  
pp. 1533-1552
Author(s):  
Kambire Famane ◽  
Gouba Elisée ◽  
Tao Sadou ◽  
Blaise Some
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Transmission Model ◽  
Acquired Immunity ◽  
Local Asymptotic Stability ◽  
Well Posed ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, we have formulated a new deterministic model to describe the dynamics of the spread of chikunguya between humans and mosquitoes populations. This model takes into account the variation in mortality of humans and mosquitoes due to other causes than chikungunya disease, the decay of acquired immunity and the immune sytem boosting. From the analysis, itappears that the model is well posed from the mathematical and epidemiological standpoint. The existence of a single disease free equilibrium has been proved. An explicit formula, depending on the parameters of the model, has been obtained for the basic reproduction number R0 which is used in epidemiology. The local asymptotic stability of the disease free equilibrium has been proved. The numerical simulation of the model has confirmed the local asymptotic stability of the diseasefree equilbrium and the existence of endmic equilibrium. The varying effects of the immunity parameters has been analyzed numerically in order to provide better conditions for reducing the transmission of the disease.

scholarly journals Allee dynamics: growth, extinction and range expansion

2017 ◽  
Author(s):  
I Bose ◽  
M Pal ◽  
C Karmakar
Keyword(s):  
Population Density ◽  
Range Expansion ◽  
Population Biology ◽  
Allee Effect ◽  
Additive Noise ◽  
Finite Population ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
One Dimension ◽  
Negative Growth

AbstractIn population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates the Allee effect in both the growth and mortality rates. In the absence of diffusion, the bifurcation diagram displays regions of both finite population density and zero population density, i.e., extinction. The early signatures of the transition to extinction at a bifurcation point are computed in the presence of additive noise. For the full RD model, the existence of travelling wave solutions of the population density is demonstrated. The parameter regimes in which the travelling wave advances (range expansion) and retreats are identified. In the weak Allee regime, the transition from the pushed to the pulled wave is shown as a function of the mortality rate constant. The results obtained are in agreement with the recent experimental observations on budding yeast populations.

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

Studies on the Ecology of the New Zealand Long-finned Eel, Anguilla dieffenbachii Gray

1952 ◽  
Vol 3 (1) ◽  
pp. 32 ◽  
Author(s):  
AMR Burnet
Keyword(s):  
New Zealand ◽  
Population Density ◽  
Mathematical Analysis ◽  
Feeding Habits ◽  
Stomach Contents ◽  
Limiting Factor ◽  
Population Densities ◽  
Baited Traps ◽  
Anguilla Dieffenbachii

Experimental trapping of eels, using carrion-baited traps, was carried out on a number of rivers of various types throughout New Zealand. Where possible, a mathematical analysis has been applied to the trapping results and an estimate of the efficiency obtained. Total trappable population densities of between 30 and 1,368 lb./ac. Were found. An attempt has been made to correlate type of river with the population density. The amount of cover present is apparently the limiting factor. The baited trap takes very few eels of less than 24 in. long and is thus not a very efficient means of keeping a stream free from eels. The feeding habits of the eel are generalized and readily adaptable to most faunas. In most rivers trout occurred only infrequently in the stomach contents.

scholarly journals Mathematical analysis of two-patch model for the dynamical transmission of tuberculosis

2012 ◽  
Vol 36 (6) ◽  
pp. 2466-2485 ◽  
Author(s):  
Jean Jules Tewa ◽  
Samuel Bowong ◽  
Boulchard Mewoli
Keyword(s):  
Mathematical Analysis ◽  
Patch Model
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