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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

where: x an oscillatory variabb; e > 0 small parameter; overdots denote differentiation with respect to timet; {3, 1coefficients of the quadratic and cubic non-linearities, respectively; ho > 0 damping viscous coefficient; h > 0, k > 0, p 2 0constants; 1 the natural frequency, e:2 D. the de tuning parameter assumed to be of order e2 • If p = 0, we have a "pure~ self-sustained system with the positive friction force (hXkX3 ). If p > 0, the mentioned system is subjected to the external excitation 3p cos 2wt in subharmonic resonance of order one-half or to the parametric one 2px cos wt in principal resonance (by fundamental we mean the cases where the natural frequency is near that of the external excitation or one-half of that of the parametric one). . The damping (negative frictiori) force is introduced to facilite the analyses andj as it will be shown below, the quadratic non_-)inearity {Jx2 is necessary in the case of external excitation. Using the asymptotic method fl], the solution of the differential equation (1.1) will be found in the form: x= acos,P+w,(a,O,¢) +s2u2(a,O,,P), a= eA1(a,O) +< A2(a,O), ' 2 0=<Bl(a,0)+• B2(a,O), ,P=wt+O (1.3)

Weak self-sustained system under the actions of less weak excitations