Two‐dimensional solvable system of difference equations with periodic coefficients
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DOI: 10.1002/mma.5780
Abstract: We show that the following two‐dimensional system of difference equations: xn+1=anxn+bnyn,yn+1=cnxn+dnyn,n∈N0, where (an)n∈N0 , (bn)n∈N0 , (cn)n∈N0 , and (dn)n∈N0 are periodic sequences, is solvable, considerably extending some results in the literature. In the case… read more here.
Keywords: system; dimensional solvable; difference equations; system difference ... See more keywords
Stability and flip bifurcation of a three‐dimensional exponential system of difference equations
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DOI: 10.1002/mma.7031
Abstract: In this paper, we study the stability of the zero equilibrium and the occurrence of flip bifurcation of the following system of difference equations: xn+1=a1ynb1+yn+c1xnek1−d1xn1+ek1−d1xn, yn+1=a2znb2+zn+c2ynek2−d2yn1+ek2−d2yn, zn+1=a3xnb3+xn+c3znek3−d3zn1+ek3−d3zn, where ai, bi, ci, di, and ki, for… read more here.
Keywords: system; difference equations; system difference; stability ... See more keywords
On the Stability of a Linear System of Difference Equations with Random Parameters
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DOI: 10.1007/s10958-018-3784-2
Abstract: We study the asymptotic behavior of solutions to a linear system of difference equation whose right-hand side at each time moment depends not only on the value at the previous moment, but also on a… read more here.
Keywords: system difference; linear system; difference equations; stability linear ... See more keywords
Global behavior of a max-type system of difference equations with four variables
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DOI: 10.1007/s12190-021-01543-8
Abstract: In this paper, we investigate global behavior of the following max-type system of difference equations with four variables $$\begin{aligned} \left\{ \begin{array}{ll}x_{n} = \max \Big \{A,\frac{z_{n-1}}{y_{n-2}}\Big \},\\ y_{n} = \max \Big \{B ,\frac{w_{n-1}}{x_{n-2}}\Big \},\\ z_{n} =… read more here.
Keywords: max type; system; max; system difference ... See more keywords
On the solutions of a max-type system of difference equations with period-two parameters
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DOI: 10.1186/s13662-018-1826-1
Abstract: AbstractIn this paper, we study the following max-type system of difference equations: {xn=max{An,yn−1xn−2},yn=max{Bn,xn−1yn−2},n∈{0,1,2,…},$$\textstyle\begin{cases}x_{n} = \max \{A_{n},\frac{y_{n-1}}{x_{n-2}} \},\\ y_{n} = \max \{B_{n} ,\frac{x_{n-1}}{y_{n-2}} \}, \end{cases}\displaystyle n\in \{0,1,2,\ldots\}, $$ where An,Bn∈(0,+∞)$A_{n},B_{n}\in(0, +\infty)$ are periodic sequences with period… read more here.
Keywords: difference equations; system; max type; type system ... See more keywords
On the solutions of a max-type system of difference equations of higher order
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DOI: 10.1186/s13662-020-02673-2
Abstract: In this paper, we study the following max-type system of difference equations of higher order: { x n = max { A , y n − t x n − s } , y n… read more here.
Keywords: difference equations; difference; max type; type system ... See more keywords
On a system of difference equations of second order solved in closed form
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DOI: 10.18514/mmn.2019.2923
Abstract: In this work we solve in closed form the system of difference equations \begin{equation*} x_{n+1}=\dfrac{ay_nx_{n-1}+bx_{n-1}+c}{y_nx_{n-1}},\; y_{n+1}=\dfrac{ax_ny_{n-1}+by_{n-1}+c}{x_ny_{n-1}},\;n=0,1,..., \end{equation*} where the initial values $x_{-1}$, $x_0$, $y_{-1}$ and $y_0$ are arbitrary nonzero real numbers and the parameters $a$,… read more here.
Keywords: system difference; difference equations; closed form; system ... See more keywords
Global asymptotic behavior of a discrete system of difference equations with delays
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DOI: 10.2298/fil2301251g
Abstract: In the present paper, we mainly investigate the qualitative behavior of the solutions of a discrete system of difference equations xn+1 = ? + Pmi =1 xn?i yn , yn+1 = ? + Pmi =1… read more here.
Keywords: system; system difference; behavior; difference equations ... See more keywords
Existence and global attractivity of periodic solutions in a max-type system of difference equations
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DOI: 10.3906/mat-1601-62
Abstract: We consider in this paper the following system of difference equations with maximum x(n+ 1) = max{f1(n, x(n)), g1(n, y(n))} , n = 0, 1, 2, . . . , y(n+ 1) = max{f2(n,… read more here.
Keywords: difference equations; existence global; system; global attractivity ... See more keywords