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Global behavior of a second-order system of difference equations

IBRAHIM YALCINKAYA|DURHASAN TURGUT TOLLU
장전수학회 (Jangjeon Mathematical Society)|2016.10|Advanced Studies in Contemporary Mathematics|제26권 제4호|pp. 653-667

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systemEquilibrium pointglobal asymptotic stabilityrate of convergencerational difference equationsemicycle
주제분류수학

초록

In this paper we investigate global asymptotic stability of unique positive equilibrium point of the system of difference equations xn+1 = x n-1y<sup>k<sub>n +1 / x n-2 +y<sup>k<sub>n , y n+1 = yn-1 x<sup>k<sub>n+1 / y n-1 +x<sup>k<sub>n , n=0, 1, ..., where the parameter k and the initial conditions x-1, x0, y-1, y0 are positive real numbers. Also, we give rate of convergence of a solution which tends to unique positive equilibrium point of the system and some numerical examples which verify our theoretical results.

Abstract

In this paper we investigate global asymptotic stability of unique positive equilibrium point of the system of difference equations xn+1 = x n-1y<sup>k<sub>n +1 / x n-2 +y<sup>k<sub>n , y n+1 = yn-1 x<sup>k<sub>n+1 / y n-1 +x<sup>k<sub>n , n=0, 1, ..., where the parameter k and the initial conditions x-1, x0, y-1, y0 are positive real numbers. Also, we give rate of convergence of a solution which tends to unique positive equilibrium point of the system and some numerical examples which verify our theoretical results.

참고문헌 (32)

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관련 논문AI추천

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