Browsing by Author "Simsek, D."

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Citation - WoS: 4
Citation - Scopus: 5
Dynamical Behavior of One Rational Fifth-Order Difference Equation
(Vasyl Stefanyk Precarpathian Natl Univ, 2023) Oğul, B.; Simsek, D.
In this paper, we study the qualitative behavior of the rational recursive equation xn+1 = +/- 1 +/- xnxn-1xn-2xn-3xn-4 xn-4 , n is an element of N0:= {0} ?N, where the initial conditions are arbitrary nonzero real numbers. The main goal of this paper, is to obtain the forms of the solutions of the nonlinear fifth-order difference equations, where the initial conditions are arbitrary positive real numbers. Moreover, we investigate stability, boundedness, oscillation and the periodic character of these solutions. The results presented in this paper improve and extend some corresponding results in the literature.
Citation - Scopus: 1
Dynamical Behavior of the Rational Difference Equation Xn+1 = Xn-13/±1 ± Xn-1Xn-3Xn-5Xn-7Xn-9Xn-11Xn-13
(Springer, 2024) Simsek, D.; Ogul, B.; Abdullayev, F. G.
Discrete-time systems are sometimes used to explain natural phenomena encountered in nonlinear sciences. We study the periodicity, boundedness, oscillation, stability, and some exact solutions of nonlinear difference equations. Exact solutions are obtained by using the standard iterative method. Some well-known theorems are used to test the stability of equilibrium points. Some numerical examples are also provided to confirm the validity of the theoretical results. The numerical component is implemented with the Wolfram Mathematica. The presented method may be simply applied to some other rational recursive issues. We explore the dynamics of adhering to the rational difference formula x(n+1) = x(n-13)/+/- 1 +/- x(n-1)x(n-3)x(n-5)x(n-7)x(n-9)x(n-11)x(n-13), where the initials are arbitrary nonzero real numbers.