Higher-order system of p-nonlinear difference equations solvable in closed-form with variable coefficients
Résumé
In this paper, we investigate the solutions of the following system of p-nonlinear difference equations
x_{n+1}^{(i)}=((a_{n}x_{n-m}^{(i+1)mod(p)})/(b_{n}+c_{n}x_{n-m}^{(i+1)mod(p)})),n,m∈N₀,p∈N,i∈{1,...,p},
where N₀=N∪{0}, the sequences (a_{n}), (b_{n}),(c_{n}), are non-zero real numbers and initial values x_{-j}^{(i)}, j∈{0,...,m}, i∈{1,...,p}, do not equal -b_{n}c_{n}⁻¹, for all n∈ N₀. Also, we investigate the behavior of positive solutions of the above-mentioned system when variable coefficients. Finally, we give some numerical examples which verify our theoretical result.
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Références
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A. S. Kurbanlı., C., Çinar and İ., Yalçinkaya. (2011a). On the behavior of positive solutions of the system of rational difference equations x_{n+1}=x_{n-1}/(y_{n}x_{n-1}+1),y_{n+1}=y_{n-1}/(x_{n}y_{n-1}+1). Mathematical and Computer Modelling, 53(5-6), 1261-1267.
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