Dynamical behavior of solution of fifteenth-order rational difference equation

Şimşek D., Oğul B., ABDULLAYEV F.

Filomat, cilt.38, sa.3, ss.997-1008, 2024 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.2298/fil2403997s
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.997-1008
  • Anahtar Kelimeler: difference equation, local stability, periodic solution, Recursive sequences
  • Uşak Üniversitesi Adresli: Hayır

Özet

Discrete-time systems are sometimes used to explain natural phenomena that happen in non-linear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations of generalized order in this paper. Using the standard iteration method, exact solutions are obtained. Some well-known theorems are used to test the stability of the equilibrium points. Some numerical examples are also provided to confirm the theoretical work’s validity. The numerical component is implemented with Wolfram Mathematica. The method presented may be simply applied to other rational recursive issues. In this research, we examine the qualitative behavior of rational recursive sequences provided that the initial conditions are arbitrary real numbers. We examine the behavior of solutions on graphs according to the state of their initial value (formula present).