On a Competitive System of Rational Difference Equations

Mehmet GÜMÜŞ

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

Makale detayları

On a Competitive System of Rational Difference Equations

Yazarlar:

Mehmet GÜMÜŞ

Yayıncı:

Emrah Evren KARA

Ana Başlıklar:

Matematik

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

12/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000670024

Sıklık:

Üç Aylık

pISSN:

2619-9653

DOI:

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

Özet:

 


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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Makale detayları

On a Competitive System of Rational Difference Equations

Yazarlar: Mehmet GÜMÜŞ

Yayıncı: Emrah Evren KARA

Ana Başlıklar: Matematik

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

Belge Tipi: Makale

Yayın Tarihi: 12/2019

Belge Dili: İngilizce

Document ID (Org No.): 2000670024

Sıklık: Üç Aylık

pISSN: 2619-9653

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

Sayı

Yazarlar:

Mehmet GÜMÜŞ

Yayıncı:

Emrah Evren KARA

Ana Başlıklar:

Matematik

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

12/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000670024

Sıklık:

Üç Aylık

pISSN:

2619-9653

DOI:

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