Modeling of Neurodegenerative Diseases Using Discrete Chaotic Systems

Parkinson's and Huntington's diseases are two of the most common neurodegenerative disorders.Tremor, muscle stiffness, and slowness of movement are symptoms of Parkinson's disease. The symptoms of Huntington's disease are severe reduction in muscle control, emotional disturbance, and pathological disorders in brain cells.These diseases are caused by destruction of the cells that secrete a substance called dopamine. In this paper,a new discrete chaotic system is introduced,which can mimic the brain's behavior for neurodegenerative diseases such as Parkinson,Huntington, and Hypokinesia. This system is described based on the similarity between the brain's behavior in normal and abnormal conditions and the chaotic systems. Bifurcation analysis is carried out with respect to different parameters, providing full spectrum of the behavior for different parameter values.Our results can be used to mathematically study the mechanisms behind these diseases.     

Characterization of the sorption behavior and mechanism of U(VI) on sericite by batch experiments and spectroscopic techniques

This study explored the sorption behavior and mechanism of U(VI) on sericite. The surface properties of sericite were investigated, and the effects of several environmental factors on U(VI) sorption to sericite were evaluated. The experimental data were simulated by different isotherm models and kinetic models. Humic acids affects U(VI) sorption obviously while silicate promotes the process in the whole pH range. The sorption–desorption hysteresis suggests an irreversible sorption process. Spectroscopic analyses indicate that the ?OH groups have an important effect in the U(VI) sorption.     

Dynamical behavior of a stochastic HBV infection model with logistic hepatocyte growth

This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.     

Stability and Hopf bifurcation analysis for an energy resource system

This paper investigates the dynamical behaviors for a four-dimensional energy resource system with time delay, especially in terms of equilibria analyses and Hopf bifurcation analysis. By setting the time delay as a bifurcation parameter, it is shown that Hopf bifurcation would occur when the time delay exceeds a sequence of critical values. Furthermore, the stability and direction of the Hopf bifurcation are determined via the normal form theory and the center manifold reduction theorem. Numerical examples are given in the end of the paper to verify the theoretical results.     

Magnetohydrodynamic effects on blood flow through an irregular stenosis

This paper investigates the magnetohydrodynamic (MHD) effects on the blood flow. Rheological properties of blood have been taken into account through the constitutive equations of a micropolar fluid. Unsteady nonlinear differential system is solved numerically by employing finite difference method. Explicit results of axial velocity, flow rate and wall shear stress are obtained and analyzed. It is found that an applied magnetic field reduces the blood flow rate. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamics of a stochastic chemostat competition model with plasmid-bearing and plasmid-free organisms

In this paper, we consider a chemostat model of competition between plasmid-bearing and plasmid-free organisms, perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Furthermore, conditions for extinction of plasmid-bearing organisms are obtained. Theoretical analysis indicates that large noise intensity $\sigma_{2}^{2}$ is detrimental to the survival of plasmid-bearing organisms and is not conducive to the commercial production of genetically altered organisms. Finally, numerical simulations are presented to illustrate the results.     

Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects

The effects of transpiration on forced convection boundary layer non-Newtonian fluid flow and heat transfer toward a linearly stretching surface are reported.The flow is caused solely by the stretching of the sheet in its own plane with a velocity varying linearly with the distance from a fixed point.The constitutive relationship for the Casson fluid is used.The governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations by using similarity transformations.Exact solutions of the resulting ordinary differential equations are obtained.The effect of increasing Casson parameter,i.e.,with decreasing yield stress(the fluid behaves as a Newtonian fluid as the Casson parameter becomes large),is to suppress the velocity field.However,the temperature is enhanced as the Casson parameter increases.It is observed that the effect of transpiration is to decrease the fluid velocity as well as the temperature.The skin-friction coefficient is found to increase as the transpiration parameter increases.     

Investigation of Q-S synchronization in coupled chaotic incommensurate fractional order systems

Chaos and synchronization in fractional order systems have received increasing attention in recent years. In this paper, the problem of Q-S synchronization for different dimensional incommensurate fractional order chaotic systems is investigated. Based on Laplace transform and stability theory of linear integer order differential systems, some synchronization schemes are designed to achieve Q-S synchronization between n-D and m-D incommensurate fractional order chaotic systems. Test problems and numerical simulations are used to show the effectiveness of the proposed approach.