论文标题
固定点的稳定性在订单的广义分数图中$ 0 <α<1 $
Stability of Fixed Points in Generalized Fractional Maps of the Orders $0< α<1$
论文作者
论文摘要
Caputo分数（带有幂律内核）和分数（Delta）差图属于更广泛定义的广义分数图，它们是具有某些幂律函数的离散卷积。本文得出的订单$ 0 <α<1 $的固定点的渐近稳定性的条件比一般的离散卷积方程的稳定性窄，而不是分数差差图的稳定性条件。分数标准图和逻辑图的得出稳定性条件与先前在数值模拟中观察到的结果一致。在非线性地图中，定点稳定性的派生限制之一与固定点 - 渐近周期两个分叉点一致。
Caputo fractional (with power-law kernels) and fractional (delta) difference maps belong to a more widely defined class of generalized fractional maps, which are discrete convolutions with some power-law-like functions. The conditions of the asymptotic stability of the fixed points for maps of the orders $0< α<1$ that are derived in this paper are narrower than the conditions of stability for the discrete convolution equations in general and wider than the well-known conditions of stability for the fractional difference maps. The derived stability conditions for the fractional standard and logistic maps coincide with the results previously observed in numerical simulations. In nonlinear maps, one of the derived limits of the fixed-point stability coincides with the fixed-point - asymptotically period two bifurcation point.
