论文标题
研究复杂顺序的低维非分数差方程的研究
Study of Low-dimensional Nonlinear Fractional Difference Equations of Complex Order
论文作者
论文摘要
我们研究了复杂顺序的分数图，$α_0e^{irπ/2} $对于$ 0 <α_0<1 $和$ 0 \ le r <1 $在1和2维度中。在二维中，我们研究了h {é}非和lozi地图，以及$ 1D $，我们研究物流，帐篷，高斯，圈子和伯努利地图。 $ 2D $的概括可以通过两种不同的方式进行，这些方式对分数订单而言并不等于，并导致不同的分叉图。我们观察到，诸如Logistic，Gauss和H {é}等光滑地图不会显示混乱，而不连续的地图（例如Lozi，Bernoulli和Circle Maps）显示混乱。帐篷图是连续的，但没有可区分，也显示了混乱。在$ 2D $中，我们发现显示混乱的复杂分数图也显示出多稳定性。因此，可以推断出，复杂分数的平滑图倾向于显示出比不连续或非差异图的更正常行为。
We study the fractional maps of complex order, $α_0e^{i r π/2}$ for $0<α_0<1$ and $0\le r<1$ in 1 and 2 dimensions. In two dimensions, we study H{é}non and Lozi map and in $1d$, we study logistic, tent, Gauss, circle, and Bernoulli maps. The generalization in $2d$ can be done in two different ways which are not equivalent for fractional-order and lead to different bifurcation diagrams. We observed that the smooth maps such as logistic, Gauss, and H{é}non maps do not show chaos while discontinuous maps such as Lozi, Bernoulli, and circle maps show chaos. The tent map is continuous but not differentiable and it shows chaos as well. In $2d$, we find that the complex fractional-order maps that show chaos also show multistability. Thus, it can be inferred that the smooth maps of complex fractional-order tend to show more regular behavior than the discontinuous or non-differentiable maps.
