Stability range of parameters at fixed points for a class of complex dynamics

We study the parameters range for the fixed point of a class of complex dynamics with the rational fractional function as $R_{n,a,c}(z)=z^n+\frac{a}{z^n}+c$, where $n=1,2,3,4$ is specified, $a$ and $c$ are two complex parameters. The relationship between two parameters, $a$ and $c$, is obtained at the fixed point. Moreover the explicit expression of the parameter $a$ and $c$ in terms of $\lambda$ is derived, where $\lambda$ is the derivative function at fixed point. The parameter regimes for the stability of the fixed point are presented numerically for some typical different cases.Comment: 15 pages, 6 figure

Suppression of epidemic spreading in complex networks by local information based behavioral responses

This work was funded by the National Natural Science Foundation of China (Grant Nos. 61473001, 11105025, and 11331009) and the Doctoral Research Foundation of Anhui University (Grant No. 02303319). Y.C.L. was supported by AFOSR under Grant No. FA9550-10-1-0083.Peer reviewedPublisher PD

N-[2-(2-Chloro­phen­yl)-2-hydroxy­ethyl]propan-2-aminium chloride

In the title compound, C11H17ClNO+·Cl−, the side chain of the ethyl­amine group is orientated approximately perpendicular to the benzene ring, the dihedral angle between the C/C/N plane of the ethyl­amine group and the benzene plane being 83.5 (3)°. In the crystal structure, inter­molecular O—H⋯Cl and N—H⋯Cl hydrogen bonds are observed. The crystal studied was an inversion twin with a 0.51 (10):0.49 (10) domain ratio

Investigation of ultra-thin Al₂O₃ film as Cu diffusion barrier on low-k (k=2.5) dielectrics

Ultrathin Al(2)O(3) films were deposited by PEALD as Cu diffusion barrier on low-k (k=2.5) material. The thermal stability and electrical properties of the Cu/low k system with Al(2)O(3) layers with different thickness were studied after annealing. The AES, TEM and EDX results revealed that the ultrathin Al(2)O(3) films are thermally stable and have excellent Cu diffusion barrier performance. The electrical measurements of dielectric breakdown and TDDB tests further confirmed that the ultrathin Al(2)O(3) film is a potential Cu diffusion barrier in the Cu/low-k interconnects system