scholarly journals Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2217
Author(s):  
Khaled S. Al Noufaey
Keyword(s):  
Growth Rate ◽  
Mortality Rate ◽  
Diffusion Coefficients ◽  
Time Delays ◽  
Equation System ◽  
Top Predator ◽  
Differential Equation System ◽  
Small Delay ◽  
The Galerkin Method ◽  
Delay Differential

In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.

scholarly journals A MATHEMATIC MODEL OF TWO MUTUALLY INTERACTING SPECIES WITH MORTALITY RATE FOR THE SECOND SPECIES

2017 ◽  
Vol 3 (2) ◽  
pp. 21-25
Author(s):  
Annisa Rahayu ◽  
Yuni Yulida ◽  
Faisal Faisal
Keyword(s):  
Mortality Rate ◽  
Interaction Model ◽  
Mathematic Model ◽  
Equation System ◽  
Differential Equation System ◽  
Interacting Species ◽  
Stability Model ◽  
Species Population ◽  
The Stability ◽  
Type Of Stability

One of the interactions that occur withinthe ecosystem is the interaction of mutualism. Such mutualism interactions can be modeled into mathematical models. Reddy (2011) study suggests a model of two mutually interacting species that assumes that each species can live without its mutualism partner. In fact, not all mutual species survive without their mutualism pairs. If it is assumed that the second species lives without its mutualism partner, the first species, then the natural growth rate of the second species population will decrease (the mortality rate). The purpose of this research is to explain the model of two mutually interacting species with mortality rate for the second species, to determine the equilibrium point and the type of stability, and to simulate them with several parameters. This research was done by way of literature studies. The result of this research is the model of two mutually interacting species with mortality rate for second species modeled using Nonlinear Differential Equation System. In the model, it was obtained 3 (three) points of equilibrium, with each type and type of stability investigated. Next up from the stability, model simulations were done. Based on several simulations conducted can be seen the value of parameters and initial values affect the population growth of both species. The interaction model of two mutual species will be stable if the first species survive and the second species over time will be extinct.

Optimal Control Problem of Vacination for The Spread of Measles Diseases Model

2018 ◽  
Vol 2 (2) ◽  
pp. 76
Author(s):  
Dani Suandi
Keyword(s):  
Optimal Control ◽  
Mortality Rate ◽  
Equation System ◽  
Vaccination Program ◽  
Control Analysis ◽  
Differential Equation System ◽  
Third Order ◽  
Vaccination Programs ◽  
The Cost ◽  
Very High

Measles is a disease in humans that is very contagious. Before the vaccine was known, the incidence of measles was very high, even the measles mortality rate reached 2.6 million every year. With the introduction of vaccines, the mortality rate in 2000-2016 can be reduced to 20.4 million deaths. Therefore, vaccination programs are very useful in reducing the incidence of measles. Unfortunately, we cannot know the optimal conditions for administering vaccines. The study of optimal control analysis of vaccination is needed in optimizing the prevention of the spread of measles. In this paper, a mathematical model which is a third-order differential equation system is constructed based on characteristic information on measles. The existence and locally stability of the equilibrium point are analyzed here. In addition, optimal control of the vaccination program also occurred. The results of our analysis suggest that the incidence of measles can decrease as the effectiveness of vaccination increases. But the effectiveness of vaccination is directly proportional to the costs incurred. If the cost incurred for the vaccination program more significant, the incidence of measles will decrease.

NONLINEAR OSCILLATIONS IN BUSINESS CYCLE MODEL WITH TIME LAGS

2000 ◽  
Vol 03 (03) ◽  
pp. 603-604 ◽  
Author(s):  
ADAM KRAWIEC ◽  
MAREK SZYDŁOWSKI ◽  
JANUSZ TOBOŁA
Keyword(s):  
Differential Equation ◽  
Business Cycle ◽  
Nonlinear Oscillations ◽  
Equation System ◽  
Hopf Bifurcations ◽  
Time Lags ◽  
Differential Equation System ◽  
Cycle Model ◽  
Business Cycle Model ◽  
Delay Differential

We analyse the Hopf bifurcations in the Kaldor–Kalecki business cycle model represented by a delay differential equation system.

Dengue and Chikungunya simulating model with mosquito periodic mortality rate

2017 ◽  
pp. 2919-2931
Author(s):  
Oscar A. Manrique A. ◽  
Steven Raigosa O. ◽  
Dalia M. Munoz P. ◽  
Mauricio Ropero P. ◽  
Anibal Munoz L. ◽  
...  
Keyword(s):  
Differential Equation ◽  
Mortality Rate ◽  
Differential Equations ◽  
Dynamic System ◽  
Ordinary Differential Equations ◽  
Equation System ◽  
Nonlinear Ordinary Differential Equations ◽  
Differential Equation System ◽  
Infectious Process ◽  
Population Mortality

A dynamic system of nonlinear ordinary differential equations to display the infectious process of Dengue-Chikungunya, is presented. The system including a mosquito periodic mortality rate and simulations of the differential equation system by MATLAB software to determine the effect of climatic variables (temperature, humidity, pluviosity) in the infectious population mortality, is carried out.

Measurement of growth rates for single crystals and pressed tablets of CuSO4.5 H2O on a rotating disc

1989 ◽  
Vol 54 (11) ◽  
pp. 2951-2961 ◽  
Author(s):  
Miloslav Karel ◽  
Jaroslav Nývlt
Keyword(s):  
Growth Rate ◽  
Single Crystal ◽  
Single Crystals ◽  
Growth Rates ◽  
Diffusion Coefficients ◽  
Preferred Orientation ◽  
Rotating Disc ◽  
Dissolution Rates ◽  
Rates Of Growth ◽  
Good Agreement

Measured growth and dissolution rates of single crystals and tablets were used to calculate the overall linear rates of growth and dissolution of CuSO4.5 H2O crystals. The growth rate for the tablet is by 20% higher than that calculated for the single crystal. It has been concluded that this difference is due to a preferred orientation of crystal faces on the tablet surface. Calculated diffusion coefficients and thicknesses of the diffusion and hydrodynamic layers in the vicinity of the growing or dissolving crystal are in good agreement with published values.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

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