具连续变量中立型差分方程的线性振动性

利用积分法研究了二阶具连续变量中立型非线性差分方程的线性振动性,即建立了此非线性差分方程和其相应的线性极限方程振动性间的联系.通过判定一个较简单的线性差分方程的振动性,就可以得到其相应非线性差分方程,甚至是一类非线性差分方程的振动性.     

一类具连续变量差分方程的强迫振动性

利用Lebesgue控制收敛定理，建立了具连续变量差分方程振动性的几个新的比较定理，给出了具连续变量差分方程强迫振动性的充分条件，并举例说明了强迫项对方程解的振动性的影响。     

一类变系数多时滞差分方程解的振动性

讨论了变系数时滞差分方程x(n 1)-x(n) ∑pi(n)x(n-ki)=0的解的振动性,并运用了一些新的技巧,在一定的条件下得到了其解振动的充分条件,并对现有文献中的某些结果进行了改进和推广.     

Pattern dynamics in cellular perception

By using a giant amoeboid cell of the Physarum plasmodium, changes in the intracellular distribution of chemical components are studied in relation to information processing in cell behavior. Various kinds of metabolites oscillate, and so the protoplasm should be a collection of chemical oscillators. Spatially, characteristic chemical patterns are self-organized for different cell shapes, and hence cell behavior. New phase waves propagate throughout the cell upon local stimulation, their direction being opposite for attraction and repulsion. Locomotion is inhibited when the coherence of the oscillators breaks. Thus, pattern dynamics is correlated with information processing in the amoeboid cell.     

Sharp oscillation and nonoscillation tests for delay dynamic equations

In this paper, we give new sufficient conditions for both oscillation and nonoscillation of the delay dynamic equation where and satisfy τ(t) ≤ σ(t) for all large t and . As an important corollary, we obtain the time scale invariant integral condition for nonoscillation: for all large t. Also, with some examples, we show that newly presented results are sharp.     

Mechanics of atoms interacting with a carbon nanotorus: optimal configuration and oscillation behaviour

In this paper, we investigate a carbon nanotorus as a caged molecular structure interacting with an atom. Assuming that the atom is located along the central axis perpendicular to the torus, the interaction energy of the system is determined using the continuum approximation together with the Lennard-Jones potential. This approach avoids the intensive computational calculations that are involved in other modelling approaches. Numerical results are presented in terms of dimensionless variables. The results show that the optimal major radius of the torus has a linear relationship with its minor radius when the atom is symmetrically situated along the torus axis. When the atom is offset from this axis, the minimum energy location shifts away from the centre as the ratio of the major and minor radii exceeds the value of 0.90. Finally, the oscillatory behaviour for the carbon atom is investigated. Our findings predict a novel nano-oscillator which can produce frequencies in the gigahertz range.     

Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.