Neimark–Sacker, flip, and transcritical bifurcation in a close‐to‐symmetric system of difference equations with exponential terms

Mylona, Chrysoula; Papaschinopoulos, G.; Schinas, C. J.

doi:10.1002/mma.7400

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2022

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“…These facts, as well as some recent interest in close‐to‐cyclic systems of difference equations (see, for example, previous works 22,28‐30 and the references therein), motivate us to investigate solvability of the following class of close‐to‐cyclic systems of difference equations

\begin{matrix} right x_{n + 3} = & left \frac{1}{a_{2} + a_{1} y_{n + 2} + a_{0} y_{n + 2} z_{n + 1}}, \\ right y_{n + 3} = & left \frac{1}{b_{2} + b_{1} z_{n + 2} + b_{0} z_{n + 2} x_{n + 1}}, \\ right z_{n + 3} = & left \frac{1}{c_{2} + c_{1} x_{n + 2} + c_{0} x_{n + 2} y_{n + 1}}, n \in ℕ_{0}, \end{matrix}

where the coefficients

a_{j}, b_{j}, c_{j}, j = \overset{0,2}{true}

, and the initial values x 1 , x 2 , y 1 , y 2 , z 1 , z 2 are real numbers.…”

Section: Introductionmentioning

confidence: 92%

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New class of three‐dimensional close‐to‐cyclic systems of difference equations solvable in closed form

Stević

2021

Math Methods in App Sciences

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\begin{matrix} right x_{n + 3} = & left \frac{1}{a_{2} + a_{1} y_{n + 2} + a_{0} y_{n + 2} z_{n + 1}}, \\ right y_{n + 3} = & left \frac{1}{b_{2} + b_{1} z_{n + 2} + b_{0} z_{n + 2} x_{n + 1}}, \\ right z_{n + 3} = & left \frac{1}{c_{2} + c_{1} x_{n + 2} + c_{0} x_{n + 2} y_{n + 1}}, n \in ℕ_{0}, \end{matrix}

where the coefficients

a_{j}, b_{j}, c_{j}, j = \overset{0,2}{true}

, and the initial values x 1 , x 2 , y 1 , y 2 , z 1 , z 2 are real numbers.…”

Section: Introductionmentioning

confidence: 92%

“…These facts, as well as some recent interest in close-to-cyclic systems of difference equations (see, for example, previous works 22,[28][29][30] and the references therein), motivate us to investigate solvability of the following class of close-to-cyclic systems of difference equations…”

Section: Introductionmentioning

confidence: 96%