English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let k , l be two integers with k ≥ 0 and l ≥ 2 , c a real number greater than or equal to 1, and f a multivariable function satisfying f ( w 1 , w 2 , w 3 , ⋯ , w l ) ≥ 0 when w 1 , w 2 ≥ 0 . We consider an arbitrary order nonlinear difference equation with the indicated function f: z n + 1 = c ( z n + z n − k ) + ( c − 1 ) z n z n − k + c f ( z n , z n − k , w 3 , ⋯ , w l ) z n z n − k + f ( z n , z n − k , w 3 , ⋯ , w l ) + c , n ≥ 0 , where initial values z − k , z − k + 1 , ⋯ , z 0 are positive and w i , i ≥ 3 , are arbitrary functions of z j , n − k ≤ j ≤ n . We classify its solutions into three types with different asymptotic behaviors, and verify the global asymptotic stability of its positive equilibrium solution z ¯ = c .

Global Behavior of an Arbitrary-Order Nonlinear Difference Equation with a Nonnegative Function