Dynamics and Expressions of Solutions of Nonlinear Difference Equations  x_(n+1)=(x_(n-3) x_(n-6))/(±x_(n-2)±x_(n-2) x_(n-3) x_(n-6) )

Burak Oğul; Dağıstan Şimşek

Makale detayları

Dynamics and Expressions of Solutions of Nonlinear Difference Equations x_(n+1)=(x_(n-3) x_(n-6))/(±x_(n-2)±x_(n-2) x_(n-3) x_(n-6) )

Yazarlar:

Burak Oğul | Dağıstan Şimşek

Yayıncı:

Sakarya University

Ana Başlıklar:

Applied Mathematics (Other)

Dergi:

Sakarya University Journal of Science Vol.29 Issue 4, pp.441-449

Belge Tipi:

Makale

Yayın Tarihi:

8/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001356311

pISSN:

2147-835X

Anahtar kelimeler:

Özet:

 Nonlinear difference equations provide a framework for modeling natural phenomena in nonlinear sciences. In this paper, we investigate the periodicity, boundedness, oscillation, stability, and exact solutions of such equations. Employing the standard iteration method, we derive closed-form solutions and analyze the stability of equilibrium points using established theorems. Numerical simulations, implemented in Wolfram Mathematica, corroborate the theoretical findings. The proposed method can be readily extended to other rational recursive problems. This paper investigates the dynamical behavior of solutions to the rational difference equation x_n1x_n-3 x_n-6x_n-2x_n-2 x_n-3 x_n-6  where the initial conditions are arbitrary nonzero real numbers. We analyze the stability properties, periodic solutions, and long-term behavior of this equation, employing both analytical and numerical approaches to characterize its dynamics.

 Nonlinear difference equations provide a framework for modeling natural phenomena in nonlinear sciences. In this paper, we investigate the periodicity, boundedness, oscillation, stability, and exact solutions of such equations. Employing the standard iteration method, we derive closed-form solutions and analyze the stability of equilibrium points using established theorems. Numerical simulations, implemented in Wolfram Mathematica, corroborate the theoretical findings. The proposed method can be readily extended to other rational recursive problems. This paper investigates the dynamical behavior of solutions to the rational difference equation x_n1x_n-3 x_n-6x_n-2x_n-2 x_n-3 x_n-6  where the initial conditions are arbitrary nonzero real numbers. We analyze the stability properties, periodic solutions, and long-term behavior of this equation, employing both analytical and numerical approaches to characterize its dynamics.

 Nonlinear difference equations provide a framework for modeling natural phenomena in nonlinear sciences. In this paper, we investigate the periodicity, boundedness, oscillation, stability, and exact solutions of such equations. Employing the standard iteration method, we derive closed-form solutions and analyze the stability of equilibrium points using established theorems. Numerical simulations, implemented in Wolfram Mathematica, corroborate the theoretical findings. The proposed method can be readily extended to other rational recursive problems. This paper investigates the dynamical behavior of solutions to the rational difference equation x_n1x_n-3 x_n-6x_n-2x_n-2 x_n-3 x_n-6  where the initial conditions are arbitrary nonzero real numbers. We analyze the stability properties, periodic solutions, and long-term behavior of this equation, employing both analytical and numerical approaches to characterize its dynamics.

 Nonlinear difference equations provide a framework for modeling natural phenomena in nonlinear sciences. In this paper, we investigate the periodicity, boundedness, oscillation, stability, and exact solutions of such equations. Employing the standard iteration method, we derive closed-form solutions and analyze the stability of equilibrium points using established theorems. Numerical simulations, implemented in Wolfram Mathematica, corroborate the theoretical findings. The proposed method can be readily extended to other rational recursive problems. This paper investigates the dynamical behavior of solutions to the rational difference equation x_n1x_n-3 x_n-6x_n-2x_n-2 x_n-3 x_n-6  where the initial conditions are arbitrary nonzero real numbers. We analyze the stability properties, periodic solutions, and long-term behavior of this equation, employing both analytical and numerical approaches to characterize its dynamics.

Makale detayları

Dynamics and Expressions of Solutions of Nonlinear Difference Equations x_(n+1)=(x_(n-3) x_(n-6))/(±x_(n-2)±x_(n-2) x_(n-3) x_(n-6) )

Yazarlar:

Burak Oğul | Dağıstan Şimşek

Yayıncı:

Sakarya University

Ana Başlıklar:

Applied Mathematics (Other)

Dergi:

Sakarya University Journal of Science Vol.29 Issue 4, pp.441-449

Belge Tipi:

Makale

Yayın Tarihi:

8/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001356311

pISSN:

2147-835X

Difference equations

Stability

Recursive sequences

Sayı

Makale detayları

Dynamics and Expressions of Solutions of Nonlinear Difference Equations x_(n+1)=(x_(n-3) x_(n-6))/(±x_(n-2)±x_(n-2) x_(n-3) x_(n-6) )

Yazarlar: Burak Oğul | Dağıstan Şimşek

Yayıncı: Sakarya University

Ana Başlıklar: Applied Mathematics (Other)

Dergi: Sakarya University Journal of Science Vol.29 Issue 4, pp.441-449

Belge Tipi: Makale

Yayın Tarihi: 8/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001356311

pISSN: 2147-835X

Difference equations

Stability

Recursive sequences

Sayı

Yazarlar:

Burak Oğul | Dağıstan Şimşek

Yayıncı:

Sakarya University

Ana Başlıklar:

Applied Mathematics (Other)

Dergi:

Sakarya University Journal of Science Vol.29 Issue 4, pp.441-449

Belge Tipi:

Makale

Yayın Tarihi:

8/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001356311

pISSN:

2147-835X