Existence of Equilibrium Points in Non-Product Spaces

1966 ◽  
Vol 14 (1) ◽  
pp. 181-190 ◽  
Author(s):  
J. Ponstein
Keyword(s):  
Equilibrium Points ◽  
Product Spaces ◽  
Existence Of Equilibrium

scholarly journals Analysis of optimal harvesting of a prey-predator fishery model with the limited sources of prey and presence of toxicity

2018 ◽  
Vol 73 ◽  
pp. 06018
Author(s):  
Sutimin ◽  
Khabibah Siti ◽  
Anies Munawwaroh Dita
Keyword(s):  
Prey Density ◽  
Equilibrium Points ◽  
Optimal Harvesting ◽  
Predator Species ◽  
Existence Of Equilibrium ◽  
Sustainable Harvesting ◽  
Toxicity Factor ◽  
The Stability ◽  
Fishery Model ◽  
Coexistence Equilibrium

A model of prey and predator species is discussed to study the effects of the limited prey density and presence of toxicity. The model is studied for sustainable optimal harvesting. The existence of equilibrium points is analyzed to find the stability of coexistence equilibrium, and use Pontryagin’s maximal method to obtain the sustainable optimal harvesting. The results show that the optimal harvesting is obtained from the solution of optimal equilibrium. The toxicity factor decreases the sustainable harvesting.

scholarly journals Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina

2021 ◽  
Vol 3 (1) ◽  
pp. 66-79
Author(s):  
Resmawan Resmawan ◽  
Agusyarif Rezka Nuha ◽  
Lailany Yahya
Keyword(s):  
Population Dynamics ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Human Class ◽  
Existence Of Equilibrium ◽  
Visual Model ◽  
The Stability ◽  
Disease Free

ABSTRAKMakalah ini membahas dinamika transmisi COVID-19 dengan melibatkan intervensi karantina. Model dikonstruksi dengan melibatkan tiga kelas penyebab infeksi, yaitu kelas manusia terpapar, kelas manusia terinfeksi tanpa gejala klinis, dan kelas manusia terinfeksi disertai gejala klinis. Variabel yang merepresentasikan intervensi karantina untuk menekan pertumbuhan infeksi juga dipertimbangkan pada model. Selanjutnya, analisis model difokuskan pada eksistensi titik kesetimbangan dan simulasi numerik untuk menunjukkan dinamika populasi secara visual. Model yang dikonstruksi membentuk model SEAQIR yang memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Analisis kestabilan menunjukkan bahwa titik kesetimbangan bebas penyakit bersifat stabil asimtotik lokal pada saat R01 dan tidak stabil pada saat R01. Simulasi numerik menunjukkan bahwa peningkatan intervensi berupa karantina dapat berkontribusi memperlambat transmisi COVID-19 sehingga diharapkan dapat mencegah terjadinya wabah pada populasi.ABSTRACTThis paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R01 and unstable at R01. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.

scholarly journals The Property of the Set of Equilibria of the Equilibrium Problem with Lower and Upper Bounds on Hadamard Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Qing-Bang Zhang ◽  
Gusheng Tang
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Points ◽  
Upper Bounds ◽  
Hadamard Manifolds ◽  
Lower And Upper Bounds ◽  
Existence Of Equilibrium ◽  
Essential Stability

The existence of equilibrium points, and the essential stability of the set of equilibrium points of the equilibrium problem with lower and upper bounds are studied on Hadamard manifolds.

scholarly journals Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina

2021 ◽  
Author(s):  
Resmawan Resmawan ◽  
Agusyarif Rezka Nuha ◽  
Lailany Yahya
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Human Class ◽  
Existence Of Equilibrium ◽  
The Stability ◽  
Disease Free

This paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R0<1 and unstable at R0>1. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.

scholarly journals Cofactors and equilibria for polynomial vector fields

2014 ◽  
Vol 144 (4) ◽  
pp. 753-760
Author(s):  
Antoni Ferragut ◽  
Jaume Llibre
Keyword(s):  
Vector Fields ◽  
Algebraic Curves ◽  
Equilibrium Points ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Differential Systems ◽  
Existence Of Equilibrium ◽  
Invariant Algebraic Curves ◽  
Exponential Factors

We present a relationship between the existence of equilibrium points of differential systems and the cofactors of the invariant algebraic curves and the exponential factors of the system.

scholarly journals Modeling the Effect of Global Warming on the Sustainable Groundwater Management: A Case Study in Bangladesh

2021 ◽  
Vol 19 ◽  
pp. 639-646
Author(s):  
Anarul Islam ◽  
Haider Ali Biswas
Keyword(s):  
Global Warming ◽  
Groundwater Level ◽  
Jacobian Matrix ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Qualitative Behavior ◽  
Existence Of Equilibrium ◽  
Linear Differential ◽  
Conditions Of Stability

The paper deals with a deterministic model for the declination of groundwater level due to deforestation and evaporation that is caused of global warming. The model is governed by three compartments by considering different level of water. The model is analyzed by finding the existence of equilibrium points and also derived the conditions of stability at the equilibrium points by using Jacobian matrix and Routh-Hurwitz criterion for the system of non-linear differential equation. We also observe the qualitative behavior by using phase portrait diagram. Finally, the numerical simulations have been performed to illustrate the effect of deforestation, poor storage of water and evaporation on the groundwater level in support of analytical findings briefly. Our study shows that, groundwater level decreases drastically due to deforestation and global warming.

Sign in / Sign up

Export Citation Format

Share Document