On a Competitive System of Rational Difference Equations

Mehmet GÜMÜŞ

doi:https://doi.org/10.32323/ujma.649122

Article Details

On a Competitive System of Rational Difference Equations

Authors:

Mehmet GÜMÜŞ

Publisher:

Emrah Evren KARA

Main Topics:

Mathematics

Journal:

Universal Journal of Mathematics and Applications 2019 Vol.2 Issue 4, pp.224-228

Document Type:

Article

Publication Date:

12/2019

Document Language:

English

Document ID (Org No.):

2000670024

Frequency:

Quarterly

pISSN:

2619-9653

DOI:

https://doi.org/10.32323/ujma.649122

Abstract:

 


This paper aims to investigate the global stability and the rate of convergence of positive solutions that converge to the equilibrium point of the system of difference equations in the modeling competitive populations in the form x(1)n+1=αx(1)n−2β+γ2∏i=0x(2)n−i, x(2)n+1=α1x(2)n−2β1+γ12∏i=0x(1)n−i, n=0,1,...xn+1(1)=αxn−2(1)β+γ∏i=02xn−i(2), xn+1(2)=α1xn−2(2)β1+γ1∏i=02xn−i(1), n=0,1,... x_{n+1}^{(1)}=\frac{\alpha x_{n-2}^{(1)}}{\beta +\gamma \prod\limits_{i=0}^{2}x_{n-i}^{(2)}},\text{ }x_{n+1}^{(2)}=\frac{\alpha _{1}x_{n-2}^{(2)}}{\beta _{1}+\gamma _{1}\prod\limits_{i=0}^{2}x_{n-i}^{(1)} }\text{, }n=0,1,...  where the parameters α,β,γ,α1,β1,γ1α,β,γ,α1,β1,γ1\alpha ,\beta ,\gamma ,\alpha _{1},\beta _{1},\gamma _{1} are positive numbers and the initial conditions x(1)−i,x(2)−ix−i(1),x−i(2) x_{-i}^{(1)},x_{-i}^{(2)} are arbitrary non-negative numbers for i∈{0,1,2}i∈{0,1,2}i\in \{0,1,2\}.

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Article Details

On a Competitive System of Rational Difference Equations

Authors: Mehmet GÜMÜŞ

Publisher: Emrah Evren KARA

Main Topics: Mathematics

Journal: Universal Journal of Mathematics and Applications 2019 Vol.2 Issue 4, pp.224-228

Document Type: Article

Publication Date: 12/2019

Document Language: English

Document ID (Org No.): 2000670024

Frequency: Quarterly

pISSN: 2619-9653

DOI: https://doi.org/10.32323/ujma.649122

Issues

Authors:

Mehmet GÜMÜŞ

Publisher:

Emrah Evren KARA

Main Topics:

Mathematics

Journal:

Universal Journal of Mathematics and Applications 2019 Vol.2 Issue 4, pp.224-228

Document Type:

Article

Publication Date:

12/2019

Document Language:

English

Document ID (Org No.):

2000670024

Frequency:

Quarterly

pISSN:

2619-9653

DOI:

https://doi.org/10.32323/ujma.649122