Fuchen Zhang

Dynamical Behaviors of a Modified Lorenz–Stenflo Chaotic System

In this paper, the ultimate bound and globally exponentially attractive sets of a modified Lorenz–Stenflo system are studied based on the Lyapunov stability theory and optimization theory. Comparing with the best results in the current literature, our new results include the existing results as special cases. Furthermore, the new results offer a theoretical support to studying the Hausdorff dimension of attractor of this modified Lorenz–Stenflo system. These theoretical results are also important and useful for chaos control and chaos synchronization.

Qualitative Study of a 4D Chaos Financial System

Some dynamics of a new 4D chaotic system describing the dynamical behavior of the finance are considered. Ultimate boundedness and global attraction domain are obtained according to Lyapunov stability theory. These results are useful in estimating the Lyapunov dimension of attractors, Hausdorff dimension of attractors, chaos control, and chaos synchronization. We will also present some simulation results. Furthermore, the volumes of the ultimate bound set and the global exponential attractive set are obtained.

On the Dynamics of the Chaotic General Lorenz System

In this paper, the global attractive sets of the general Lorenz system are studied based on the Lyapunov stability theory and optimization theory. The innovation of this paper lies in that the method of constructing Lyapunov functions applied to many other dynamical systems is not applicable to this general Lorenz system. Comparing with the best results in the current literature, our new results fill the gap of the estimate for the case of a > 0, c > 0, b > 1.

Analysis of a Generalized Lorenz–Stenflo Equation

Although the globally attractive sets of a hyperchaotic system have important applications in the fields of engineering, science, and technology, it is often a difficult task for the researchers to obtain the globally attractive set of the hyperchaotic systems due to the complexity of the hyperchaotic systems. Therefore, we will study the globally attractive set of a generalized hyperchaotic Lorenz–Stenflo system describing the evolution of finite amplitude acoustic gravity waves in a rotating atmosphere in this paper. Based on Lyapunov-like functional approach combining some simple inequalities, we derive the globally attractive set of this system with its parameters. The effectiveness of the proposed methods is illustrated via numerical examples.

A novel preparation of milk protein/polyethylene terephthalate fabric

In this work, -NH2 groups were introduced to polyethylene terephthalate (PET) fibers by nitration and reduction method, and then milk protein was grafted on the nitrated and reduced PET (NR PET) fibers by sucrose glycidyl ether crosslinking agent. FTIR suggested the milk protein was successfully grafted on PET fiber surface. SEM images showed a layer of substance covered on the PET fiber surface. DSC demonstrated an excellent thermal stability of milk protein/PET fiber. The moisture regain was improved by milk protein/PET fiber. Moreover, the crease recovery angle and stiffness were retained by the milk protein/PET fabric.

Preparation and dyeing of super hydrophilic polyethylene terephthalate fabric

In this study, the dyeing properties of PET fabrics modified with sulfuric acid was investigated using disperse red E-4B and disperse blue 2BLNG-L at high temperature and high pressure. The results revealed that the sulfuric acid modification improved the K/S value of dyeing PET fabrics, and the modified PET fabric could be dyed uniformly. The a, b, C, L and H of modified PET fabric were almost the same as that of original PET fabric. The water contact angles were still 0o after 10s, indicating that the hydrophilic property of modified PET fabrics still kept excellent. The wash fastness of dyed PET fabrics after modification was generally good.

The preparation of flame-retardant poly (ethylene terephthalate) fabric by ionic agent

In this paper, PET fabric was modified by the flame retardant HOP to improve flame retardance. The results showed that the flame retardance of PET fabric improved a lot. With the increase of the HOP concentration, the limiting oxygen index could increase to 34%, the horizontal burning length could decrease to 0 mm, the horizontal burning rate could decrease to 0 mm/s, and the vertical ignite time could increase to 5 s. The infrared spectroscopy showed the modification of HOP made PET fabric gain phosphate groups. Moreover, the breaking strength, stiffness and crease recovery angle were kept well.

On the New Results of Global Exponential Attractive Sets of the T Chaotic System

In this paper, the global exponential attractive sets of the T chaotic system are studied. The method for constructing Lyapunov functions that are applied to the former chaotic systems [Liao, 2004; Liao et al., 2008; Wang et al., 2011; Zhang et al., 2011a; Zhang et al., 2011b; Yu & Liao, 2008; Li et al., 2009; Yu et al., 2009] does not work for the T chaotic system. We overcome this difficulty by introducing a cross term xy. We get a perfect result that contains the case for the parameter values considered covering the most interesting case of the chaotic attractor system.