2017
DOI: 10.22436/jnsa.011.01.07
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On the rational difference equation y n + 1 = α 0 y n + α 1 y n − p + α 2 y n − q + α 3 y n − r + α 4 y n − s β 0 y n + β 1 y n − p + β 2 y n − q + β 3 y n − r + β 4 y n − s

Abstract: In this paper, we examine and explore the boundedness, periodicity, and global stability of the positive solutions of the rational difference equationwhere the coefficients α i , β i ∈ (0, ∞), i = 0, 1, 2, 3, 4, and p, q, r, and s are positive integers. The initial conditions y −s ,. . . ,y −r ,. . . , y −q ,. . . , y −p ,. . . ,y −1 ,y 0 are arbitrary positive real numbers such that p < q < r < s. Some numerical examples will be given to illustrate our result.

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Cited by 6 publications
(7 citation statements)
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“…It is based on insights from complex systems science, adept at understanding non-linear developments and ‘Black Swan’ events, 1 while offering a fresh perspective on policy formulation. By weaving together insights from managerial practice ( Snowden and Boone, 2007 ; Joint Research Centre, European Commission et al, 2021 ), risk management ( Taleb et al, 2014 ; Taleb, 2020 ), and the framework of attractor landscapes in human behavior change ( Heino et al, 2022 ), this work aims to build on calls to craft policies suitable for an interconnected world ( Heino et al, 2023 ).…”
Section: Risk Responses In a Complex Worldmentioning
confidence: 99%
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“…It is based on insights from complex systems science, adept at understanding non-linear developments and ‘Black Swan’ events, 1 while offering a fresh perspective on policy formulation. By weaving together insights from managerial practice ( Snowden and Boone, 2007 ; Joint Research Centre, European Commission et al, 2021 ), risk management ( Taleb et al, 2014 ; Taleb, 2020 ), and the framework of attractor landscapes in human behavior change ( Heino et al, 2022 ), this work aims to build on calls to craft policies suitable for an interconnected world ( Heino et al, 2023 ).…”
Section: Risk Responses In a Complex Worldmentioning
confidence: 99%
“…A landscape with only one possible attractor feels safe. But it is crucial to understand that, had a transition to ruin happened, the current discourse would not take place – a prime example of survivorship bias in the absence of the aforementioned black swan events ( Taleb, 2007 ; Taleb et al, 2014 ). The absence of a previous leap from one attractor to a disastrous one by no means negates its potential occurrence in the future.…”
Section: Attractors and Tipping Points In The Space Of Possibilitiesmentioning
confidence: 99%
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“…Yet the drivers of the invasive transition remain poorly characterized, obscuring the reliable identification of high-risk lesions (Wilson et al, 2022;Wang et al, 2024). In IDC, neoplastic epithelial cells have breached through the basement membrane and evaded the ductal confinement into the surrounding stromal tissue (Lo et al, 2017;Wilson et al, 2022;Wang et al, 2024). The transition from DCIS to IDC is initiated by a subset of transformed cells that unlock the restricted capacity of phenotypic plasticity.…”
Section: Introductionmentioning
confidence: 99%
“…Animal cell imaging usually has been applied for various biomedical applications, namely targeted drug delivery toward tumours [23], biolabeling and bioimaging [24], disease detection and so forth [24].…”
Section: Introductionmentioning
confidence: 99%