Face-centred cubic to body-centred cubic phase transformation under [1 0 0] tensile loading

Molecular dynamics simulation was used to verify a speculation of the existence of a certain face-centred cubic (FCC) to body-centred cubic (BCC) phase transformation pathway. Four FCC metals, Ni, Cu, Au and Ag, were stretched along the [1?0?0] direction at various strain rates and temperatures. Under high strain rate and low temperature, and beyond the elastic limit, the bifurcation of the FCC phase occurred with sudden contraction along one lateral direction and expansion along the other lateral direction. When the lattice constant along the expansion direction converged with that of the stretched direction, the FCC phase transformed into an unstressed BCC phase. By reducing the strain rate or increasing the temperature, dislocation or ‘momentum-induced melting’ mechanisms began to control the plastic deformation of the FCC metals, respectively.     

Bogdanov-Takens Bifurcation in a Host-parasitoidModel

In this paper, we study a host-parasitoid model with Holling II Functional response, where we focus on a special case: the carrying capacity K2 for parasitoids is equal to a critical valuer 1η. It is shown that the model can undergo Bogdanov-Takens bifurcation. The approximate expressions forsaddle-node, Homoclinic and Hopf bifurcation curves are calculated. Numerical simulations, including bifurcation diagrams and corresponding phase portraits, are also given to illustrate the theoretical results.     

Dynamical analysis of age-structured pertussis model with covert infection

An age-structured pertussis model with covert infection is proposed to understand the effect of covert infection on the recurrence of pertussis. It is found that vaccination only for young children does not have a decisive effect on whooping cough control. It is shown that although the vaccine coverage rate is relatively high, the model has a backward bifurcation for a larger covert infection rate. In addition, sufficient conditions for the disease-free steady state to be globally asymptotically stable are obtained.     

Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.     

Leibniz Conformal Algebras of Rank Two

We classify all Leibniz conformal algebras of rank two.     

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.     

A semiflexible polymer ring acting as a nano-propeller

The dynamics of a rotating elastic nano-ring driven in a viscous fluid by an externally applied torque about a specific axis is studied using elasto-hydrodynamic simulations. We show that a helical deformation of the ring filament is excited, and that this leads to directed propulsion which is independent of the direction of rotation. It is found that the propulsive force and efficiency initially increase as the torque is increased, and then decrease discontinuously at a buckling transition at a critical torque. This unique propulsive behavior at the shape transition arises due to its specific geometry, i.e., circularity of an elastic filament. The implications of the behavior for artificial microscopic devices are discussed.     

一类余维3的鞍-焦点异宿环分支

对余维3系统X_μ(x)具有包含一个双曲鞍-焦点O_1和一个非双曲鞍-焦点O_2的异宿环f进行了研究.证明了在f的邻域内有可数无穷条周期轨线和异宿轨线,当非粗糙异宿轨线Γ~0破裂时X_μ(x)会产生同宿轨分支,并给出了相应的分支曲线和两种同宿环共存的参数值.在3参数扰动下Γ~0破裂和O_2点产生Hopf分支的情况下,在f的邻域内有一条含O_1点同宿环,可数无效多条的轨线同宿于O_2点分支出的闭轨H_0,一条或无穷多条(可数或连续统的)异宿轨线等.     

BIFURCATION OF CUBIC INTEGRABLE SYSTEM UNDER CUBIC PERTURBATION

In this paper, we consider the bifurcation for a class of cubic integrable system under cubic perturbation. Using bifurcation theory and qualitative analysis, we obtain a complete bifurcation diagram of the system in a neighbourhood of the origin for parameter plane.     

Analysis of transition between chaos and hyper-chaos of an improved hyper-chaotic system

An improved hyper-chaotic system based on the hyper-chaos generated from Chen's system is presented, and some basic dynamical properties of the system are investigated by means of Lyapunov exponent spectrum, bifurcation diagrams and characteristic equation roots. Simulations show that the new improved system evolves into hyper-chaotic, chaotic, various quasi-periodic or periodic orbits when one parameter of the system is fixed to be a certain value while the other one is variable. Some computer simulations and bifurcation analyses are given to testify the findings.