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

We study the fractional maps of complex order, $\alpha_0e^{i r \pi/2}$ for$0<\alpha_0<1$ and $0\le r<1$ in 1 and 2 dimensions. In two dimensions, westudy H{\'e}non and Lozi map and in $1d$, we study logistic, tent, Gauss,circle, and Bernoulli maps. The generalization in $2d$ can be done in twodifferent ways which are not equivalent for fractional-order and lead todifferent bifurcation diagrams. We observed that the smooth maps such aslogistic, Gauss, and H{\'e}non maps do not show chaos while discontinuous mapssuch as Lozi, Bernoulli, and circle maps show chaos. The tent map is continuousbut not differentiable and it shows chaos as well. In $2d$, we find that thecomplex fractional-order maps that show chaos also show multistability. Thus,it can be inferred that the smooth maps of complex fractional-order tend toshow more regular behavior than the discontinuous or non-differentiable maps.

Study of Low-dimensional Nonlinear Fractional Difference Equations of Complex Order