Global asymptotic stability of a nonlinear recursive sequence
Copyright policy )Global asymptotic stability of a nonlinear recursive sequence
Using a ``semicycle analysis method'' developed by the authors, they prove that the positive equilibrium of the nonlinear difference equation \[ x_{n+1}=\frac{x_nx_{n-1}^b+x_{n-2}^b+a}{x_{n-1}^b+x_nx_{n-2}^b+a}, \quad n\geq 0 \] is globally asymptotically stable for parameters \(a\geq 0\), \(b>0\) and initial values \(x_{-2},x_{-1},x_0>0\).
- East China Normal University China (People's Republic of)
- University of South China China (People's Republic of)
Global asymptotic stability, positive equilibrium, Stability of difference equations, Multiplicative and other generalized difference equations, Applied Mathematics, Semicycle, semicycle analysis method, nonlinear difference equation, recursive difference equation, Recursive difference equation, global asymptotic stability
Global asymptotic stability, positive equilibrium, Stability of difference equations, Multiplicative and other generalized difference equations, Applied Mathematics, Semicycle, semicycle analysis method, nonlinear difference equation, recursive difference equation, Recursive difference equation, global asymptotic stability
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).17 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!