scholarly journals Dynamics of General Class of Difference Equations and Population Model with Two Age Classes

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 516 ◽  
Author(s):  
Osama Moaaz ◽  
George E. Chatzarakis ◽  
Dimplekumar Chalishajar ◽  
Omar Bazighifan
Keyword(s):  
Global Stability ◽  
Difference Equations ◽  
General Class ◽  
Population Model ◽  
Qualitative Behavior ◽  
Age Classes ◽  
Numerical Examples ◽  
Local And Global Stability ◽  
Period 2

In this paper, we study the qualitative behavior of solutions for a general class of difference equations. The criteria of local and global stability, boundedness and periodicity character (with period 2 k ) of the solution are established. Moreover, by applying our general results on a population model with two age classes, we establish the qualitative behavior of solutions of this model. To support our results, we introduce some numerical examples.

scholarly journals Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Karim Khan ◽  
Rahat Zarin ◽  
Amir Khan ◽  
Abdullahi Yusuf ◽  
Mohammed Al-Shomrani ◽  
...  
Keyword(s):  
Global Stability ◽  
Equilibrium Point ◽  
Lyapunov Theory ◽  
Endemic Equilibrium ◽  
Qualitative Behavior ◽  
Geometrical Approach ◽  
Local And Global Stability ◽  
Free Case ◽  
Compound Matrix ◽  
Disease Free

AbstractIn this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative behavior. We derive the threshold number $R_{0}$ R 0 of the model using the next generation method. In the disease-free case, we carry out the local and global stability under the condition $R_{0}<1$ R 0 < 1 . Moreover, we derive the global stability at the disease-free equilibrium point by utilizing the Castillo-Chavez method. On the other hand, at the endemic equilibrium point, we show the local and global stability to be held under specific conditions and $R_{0}>1$ R 0 > 1 . We also establish the global stability at the endemic equilibrium point with the help of a geometrical approach, which is a generalization of Lyapunov theory, by using a second additive compound matrix. Finally, we take into account the sensitivity analysis of the threshold number with other parameters. We also discuss several graphs of important parameters.

scholarly journals The Dynamics of the Solutions of Some Difference Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
H. El-Metwally ◽  
R. Alsaedi ◽  
E. M. Elsayed
Keyword(s):  
Difference Equation ◽  
Global Stability ◽  
Difference Equations ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Global Behavior ◽  
Local And Global Stability ◽  
Rational Difference Equation

This paper is devoted to investigate the global behavior of the following rational difference equation:yn+1=αyn-t/(β+γ∑i=0kyn-(2i+1)p∏i=0kyn-(2i+1)q),  n=0,1,2,…, whereα,β,γ,p,q∈(0,∞)andk,t∈{0,1,2,…}with the initial conditionsx0,  x-1,…,  x-2k,  x-2max {k,t}-1∈ (0,∞). We will find and classify the equilibrium points of the equations under studying and then investigate their local and global stability. Also, we will study the oscillation and the permanence of the considered equations.

scholarly journals Some Qualitative Behavior of Solutions of General Class of Difference Equations

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 585 ◽  
Author(s):  
Osama Moaaz ◽  
Dimplekumar Chalishajar ◽  
Omar Bazighifan
Keyword(s):  
Periodic Solution ◽  
Asymptotic Behavior ◽  
Asymptotic Stability ◽  
Difference Equations ◽  
General Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Qualitative Behavior ◽  
Local Asymptotic Stability ◽  
Necessary And Sufficient

In this work, we consider the general class of difference equations (covered many equations that have been studied by other authors or that have never been studied before), as a means of establishing general theorems, for the asymptotic behavior of its solutions. Namely, we state new necessary and sufficient conditions for local asymptotic stability of these equations. In addition, we study the periodic solution with period two and three. Our results essentially extend and improve the earlier ones.

scholarly journals Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey

Diversity ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 23
Author(s):  
Jawdat Alebraheem
Keyword(s):  
Global Stability ◽  
Stability Conditions ◽  
Dynamic Behaviors ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Predator Prey Model ◽  
Prey Model ◽  
Proposed Model

In this article, the use of predator-dependent functional and numerical responses is proposed to form an autonomous predator–prey model. The dynamic behaviors of this model were analytically studied. The boundedness of the proposed model was proven; then, the Kolmogorov analysis was used for validating and identifying the coexistence and extinction conditions of the model. In addition, the local and global stability conditions of the model were determined. Moreover, a novel idea was introduced by adding the oscillation of the immigration of the prey into the model which forms a non-autonomous model. The numerically obtained results display that the dynamic behaviors of the model exhibit increasingly stable fluctuations and an increased likelihood of coexistence compared to the autonomous model.

scholarly journals Discrete three-stage population model: persistence and global stability results

2008 ◽  
Vol 2 (4) ◽  
pp. 415-427 ◽  
Author(s):  
Azmy S. Ackleh ◽  
Patrick De Leenheer
Keyword(s):  
Global Stability ◽  
Population Model ◽  
Stability Results ◽  
Model Persistence

scholarly journals A note on the global stability of generalized difference equations

2002 ◽  
Vol 15 (6) ◽  
pp. 655-659 ◽  
Author(s):  
E. Liz ◽  
J.B. Ferreiro
Keyword(s):  
Global Stability ◽  
Difference Equations
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