scholarly journals A Three Species Ecological Model with a Predator and Two Preying Species

2016 ◽  
Vol 9 ◽  
pp. 26-32
Author(s):  
Tripuraribhatla Vidyanath ◽  
K. Lakshmi Narayan ◽  
Shahnaz Bathul
Keyword(s):  
Numerical Simulation ◽  
Analytical Study ◽  
Ecological Model ◽  
Equilibrium Points ◽  
The Other ◽  
Positive Equilibrium ◽  
First Order ◽  
Alternate Food ◽  
Linear Differential ◽  
Positive Equilibrium Point

The present paper is devoted to an analytical study of a three species ecological model in which a predator is preying on the other two species which are mutually helping each other. In addition to that, all the three species are provided with an alternate food. The model is characterized by a set of first order non-linear differential equations. All the possible equilibrium points of the model have been derived and the local and global stability for the positive equilibrium point is discussed and supported by the numerical simulation using the MATLAB.

scholarly journals “Stability Analysis of Three Species Ammensalism Model with Time Delay”

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3664-3670
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Time Delay ◽  
Global Stability ◽  
Analytical Study ◽  
Present Model ◽  
Ecological Model ◽  
Equilibrium Points

The present model is devoted to an analytical study of a three species syn-ecological model which the 1 st species ( ) N1 ammensal on the 2 nd species ( ) N2 and 2 nd species ( ) N2 ammensal on the 3 rd species ( ) N3 . Here 1 st species and 2 nd species are neutral to each other. A time delay is established between 1 st species and 2 nd species and 2 nd species and 3rd species. All attainable equilibrium points of the model are known and native stability for each case is mentioned and also the global stability of co-existing state is discussed by constructing appropriate Lyapunov operate. Further, precise solutions of perturbed equations are derived. The steadiness analysis is supported by numerical simulation victimization MatLab.

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.

scholarly journals A Three Species Ecological Model with a Prey, Predator and Competitor to the Predator and Optimal Harvesting of the Prey

2012 ◽  
Vol 1 ◽  
pp. 21-32
Author(s):  
A.V. Papa Rao ◽  
K. Lakshmi Narayan ◽  
Shahnaz Bathul
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Single Species ◽  
Analytical Investigation ◽  
Optimal Harvesting ◽  
Stability Criteria ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Analytical Stability ◽  
The Stability

The present paper is devoted to an analytical investigation of three species ecological model with a Prey (N1), a predator (N2) and a competitor (N3) to the Predator without effecting the prey (N1). in addition to that, the species are provided with alternative food. The model is characterized by a set of first order non-linear ordinary differential equations. All the eight equilibrium points of the model are identified and local and global stabilitycriteria for the equilibrium states except fully washed out and single species existence are discussed. Further exact solutions of perturbed equations have been derived. The analytical stability criteria are supported by numerical simulations using mat lab. Further we discussed the effect of optimal harvesting on the stability.

scholarly journals Location of triangular equilibrium points in the perturbed CR3BP with laser radiation pressure and oblateness

2018 ◽  
Vol 6 (1) ◽  
pp. 8
Author(s):  
Nabawia Khalifa
Keyword(s):  
Laser Radiation ◽  
Radiation Pressure ◽  
Analytical Study ◽  
Equilibrium Points ◽  
Laser Beam Propagation ◽  
Three Body Problem ◽  
Numerical Application ◽  
Triangular Points ◽  
First Order ◽  
Three Body

This paper represents a semi-analytical study of the effect of ground-based laser radiation pressure on the location of triangular points in the framework of the planar circular restricted three-body problem (CR3BP). The formulation includes both the effects of oblateness of J2 in addition to laser radiation pressure, where laser’s disturbing function expanded in Legendre polynomials up to the first order. Earth-Moon system is considered in which a laser station is located on Earth and sends laser beams toward the infinitesimal body. The model takes into account the effect of Earth's atmosphere on laser beam propagation. The numerical application emphasis that the location of the triangular points affected by the considered perturbations.

Conformable Fractional SEIR Epidemic Model With Treatment

2021 ◽  
Vol 14 ◽  
Author(s):  
Arti Malik ◽  
Nitendra Kumar ◽  
Khursheed Alam
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Epidemic Model ◽  
Analytical Study ◽  
Equilibrium Points ◽  
Treatment Modalities ◽  
Local Asymptotic Stability ◽  
Fractional Differential ◽  
Disease Free

Background: The present paper is based on models of conformable fractional differential equation to describe the dynamics of certain epidemics. Methods: In this paper we have divided the population in the susceptible, exposed, infectious, recovered and also describe the treatment modalities. Results: The analytical study of the model show two equilibrium points (disease free equilibrium and endemic equilibrium). Conclusion: For both cases local asymptotic stability has been proven. In the conclusion we have presented the numerical simulation.

scholarly journals On Stationary Solutions Of Delay Differential Equations: A Model Of Local Translation In Synapses

2019 ◽  
Vol 14 (2) ◽  
pp. 554-569 ◽  
Author(s):  
V.A. Likhoshvai ◽  
T.M. Khlebodarova
Keyword(s):  
Equilibrium Point ◽  
Relative Stability ◽  
Equilibrium Points ◽  
Stationary Solutions ◽  
Translation System ◽  
Positive Equilibrium ◽  
Absolute Instability ◽  
Local Translation ◽  
Delayed Arguments ◽  
Positive Equilibrium Point

The results of analytical analysis of stationary solutions of a differential equation with two delayed arguments τ1 and τ2 are presented. Such equations are used in modeling of molecular-genetic systems where the delay of arguments appear naturally. Conditions of existence of non-negative solutions are described, and dependence of stability of these solutions on the values of delayed arguments is studied. This stability theory allows to give complete characterization of these solutions for all values of the parameters of the model, and ensures instability of a positive equilibrium point for any values of the delays τ2 ≥ τ1 ≥ 0 in the case when it is unstable for τ2 = τ1 = 0 (absolute instability). If this positive equilibrium point is stable only for τ2 = τ1 = 0, then this domain τ2 ≥ τ1 ≥ 0 is the domain of absolute instability as well. For positive equilibrium points which are stable at τ2 = τ1 = 0, we find domains of absolute stability were the equilibrium points remain stable for all values of the parameters τ1 and τ2. The domains of relative stability, where these points become unstable for some values of these parameters are also described. We show that when the efficiency of translation, and non-linearity and complexity of its regulation mechanisms grow, the domains of the absolute and relative stability of the positive equilibrium point shrink, while the domains of its instability expand. So, enhanced activity of the local translation system can be a factor of its instability and that of the risk of neuro-psychical diseases related to distortions of plasticity of the synapse and memory, where importance of stability of the proteome in the synapse is postulated.

scholarly journals Evaluation of the Number of Visits to Chinese Medical Institutions Using a Logistic Differential Equation Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Xiaoxia Zhao ◽  
Wei Li ◽  
Yanyang Wang ◽  
Lihong Jiang
Keyword(s):  
Differential Equation ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Equation Model ◽  
Positive Equilibrium ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Differential Equation Model ◽  
Number Of Visits ◽  
Positive Equilibrium Point

In this study, we established a two-dimensional logistic differential equation model to study the number of visits in Chinese PHCIs and hospitals based on the behavior of patients. We determine the model's equilibrium points and analyze their stability and then use China medical services data to fit the unknown parameters of the model. Finally, the sensitivity of model parameters is evaluated to determine the parameters that are susceptible to influence the system. The results indicate that the system corresponds to the zero-equilibrium point, the boundary equilibrium point, and the positive equilibrium point under different parameter conditions. We found that, in order to substantially increase visits to PHCIs, efforts should be made to improve PHCI comprehensive capacity and maximum service capacity.

A model of neuronal bursting using three coupled first order differential equations

1984 ◽  
Vol 221 (1222) ◽  
pp. 87-102 ◽  
Keyword(s):  
Phase Plane ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Model Neuron ◽  
Recent Model ◽  
The Other ◽  
Stable Equilibrium Point ◽  
General Phenomenon ◽  
First Order ◽  
First Order Differential Equations

We describe a modification to our recent model of the action potential which introduces two additional equilibrium points. By using stability analysis we show that one of these equilibrium points is a saddle point from which there are two separatrices which divide the phase plane into two regions. In one region all phase paths approach a limit cycle and in the other all phase paths approach a stable equilibrium point. A consequence of this is that a short depolarizing current pulse will change an initially silent model neuron into one that fires repetitively. Addition of a third equation limits this firing to either an isolated burst or a depolarizing afterpotential. When steady depolarizing current was applied to this model it resulted in periodic bursting. The equations, which were initially developed to explain isolated triggered bursts, therefore provide one of the simplest models of the more general phenomenon of oscillatory burst discharge.

A prey - partially dependent predator with a reserved zone: modelling and analysis

2015 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
M.V. Ramana Murthy ◽  
Dahlia Khaled
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Function ◽  
Functional Response ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
The Other ◽  
Local Bifurcation ◽  
Control Parameters ◽  
Persistence Conditions

<p>In this paper, a mathematical model consisting of a prey-partially dependent predator has been proposed and analyzed. It is assumed that the prey moving between two types of zones, one is assumed to be a free hunting zone that is known as an unreserved zone and the other is a reserved zone where hunting is prohibited. The predator consumes the prey according to the Beddington-DeAngelis type of functional response. The existence, uniqueness and boundedness of the solution of the system are discussed. The dynamical behavior of the system has been investigated locally as well as globally with the help of Lyapunov function. The persistence conditions of the system are established. Local bifurcation near the equilibrium points has been investigated. Finally, numerical simulation has been used to specify the control parameters and confirm the obtained results.</p>

Dynamics of a prey predator disease model with Holling type functional response and stochastic perturbation

2020 ◽  
pp. 471-488
Author(s):  
M. N. Srinivas ◽  
G. Basava Kumar ◽  
V. Madhusudanan
Keyword(s):  
Equilibrium Point ◽  
Disease Model ◽  
Stochastic Perturbation ◽  
Positive Equilibrium ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Unique Positive Solution ◽  
Stochastic Nature ◽  
Research Article ◽  
Positive Equilibrium Point

The present research article constitutes Holling type II and IV diseased prey predator ecosystem and classified into two categories namely susceptible and infected predators.We show that the system has a unique positive solution. The deterministic and stochastic nature of the dynamics of the system is investigated. We check the existence of all possible steady states with local stability. By using Routh-Hurwitz criterion we showed that the positive equilibrium point $E_{7}$ is locally asymptotically stable if $x^{*} > \sqrt{m_{1}}$ .Moreover condition of the global stability of positive equilibrium point $E_{7}$ are also entrenched with help of Lyupunov theorem. Some Numerical simulations are carried out to illustrate our analytical findings.

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