DCDS

For the Gylden-Meshcherskii-type problem with a
periodically cha-nging gravitational parameter, we prove the
existence of radially periodic solutions with high angular
momentum, which are Lyapunov stable in the radial direction.

DCDS

In this paper, we study the Cauchy problem of a higher-order *μ*-Camassa-Holm equation. We first establish the Green's function of $(μ-\partial_{x}^{2}+\partial_{x}^{4})^{-1}$ and local well-posedness for the equation in Sobolev spaces $H^{s}(\mathbb{S})$, $s>\frac{7}{2}$. Then we provide the global existence results for strong solutions and weak solutions. Moreover, we show that the solution map is non-uniformly continuous in $H^{s}(\mathbb{S})$, $s≥ 4$. Finally, we prove that the equation admits single peakon solutions which have continuous second derivatives and jump discontinuities in the third derivatives.

DCDS-B

We study the prevalence of stable periodic solutions of the forced relativistic pendulum equation for external force which guarantees the existence of periodic solutions. We prove the results for a general planar system.

DCDS

We study the existence and stability of periodic solutions of two kinds of regular equations by means of classical topological techniques like the Kolmogorov-Arnold-Moser (KAM) theory, the Moser twist theorem, the averaging method and the method of upper and lower solutions in the reversed order. As an application, we present some results on the existence and stability of $ T$-periodic solutions of a Liebau-type equation.

NACO

We introduce two set cover problems with submodular costs and linear/submodular penalties and
offer two approximation algorithms of ratios $\eta$ and $2\eta$ respectively via the primal-dual
technique, where $\eta$ is the largest number of sets that each element belongs to.

DCDS-B

In recent years, online social networks such as Twitter, have become a major source of information exchange and research on information diffusion in social networks has been accelerated. Partial differential equations are proposed to characterize temporal and spatial patterns of information diffusion over online social networks. The new modeling approach presents a new analytic framework towards quantifying information diffusion through the interplay of structural and topical influences. In this paper we develop a non-autonomous diffusive logistic model with indefinite weight and the Robin boundary condition to describe information diffusion in online social networks. It is validated with a real dataset from an online social network, Digg.com. The simulation shows that the logistic model with the Robin boundary condition is able to more accurately predict the density of influenced users. We study the bifurcation, stability of the diffusive logistic model with heterogeneity in distance. The bifurcation and stability results of the model information describe either information spreading or vanishing in online social networks.

DCDS-B

In this paper, we propose a mathematical model to describe the avian
influenza dynamics in wild birds with bird mobility and
heterogeneous environment incorporated. In addition to establishing
the basic properties of solutions to the model, we also prove the
threshold dynamics which can be expressed either by the basic
reproductive number or by the principal eigenvalue of the
linearization at the disease free equilibrium. When the environment
factor in the model becomes a constant (homogeneous environment), we
are able to find explicit formulas for the basic reproductive
number and the principal eigenvalue. We also perform numerical
simulation to explore the impact of the heterogeneous environment on
the disease dynamics. Our analytical and numerical results reveal
that the avian influenza dynamics in wild birds is highly affected
by both bird mobility and environmental heterogeneity.

CPAA

In this paper we construct a mathematical model of two microbial
populations competing for a single-limited nutrient with internal
storage in an unstirred chemostat. First we establish the existence
and uniqueness of steady-state solutions for the single population.
The conditions for the coexistence of steady states are determined.
Techniques include the maximum principle, theory of bifurcation and
degree theory in cones.

DCDS-B

In this paper, we analyze a system modeling the growth of single phytoplankton populations in a water column, where population
growth increases monotonically with the nutrient
quota stored within individuals. We establish a threshold result on
the global extinction and persistence of phytoplankton. Condition for persistence is shown to depend on the
principal eigenvalue of a boundary value problem, which is related to the physical transport
properties of the water column (i.e. the diffusivity and the sinking speed), nutrient uptake rate, and growth rate.

DCDS-B

In this paper, we investigate two-vessel gradostat models describing the
dynamics of harmful algae with seasonal temperature variations, in
which one vessel represents a small cove connected to a larger lake. We
first define the basic reproduction number for the model system, and
then show that the trivial periodic state is globally asymptotically
stable, and algae is washed out eventually if the basic
reproduction number is less than unity, while there exists at least
one positive periodic state and algal blooms occur when it is
greater than unity. There are several types of productions for dissolved toxins, related to the algal growth rate, and nutrient limitation, respectively. For the system with a specific toxin production, the global attractivity of
positive periodic steady-state solution can be established. Numerical simulations from the basic reproduction number
show that the factor of seasonality plays an important role in the
persistence of harmful algae.