Acta Mathematicae Applicatae Sinica, English Series最新文献

The stable switching phenomenon of a diffusion mussel-algae system with two delays and half saturation constant is studied. The stability of positive equilibrium and the existence of Hopf bifurcation on two-delay plane are investigated by calculating the stability switching curves. The normal form on the central manifold near Hopf bifurcation point is also derived. It can find that two different delays can induce the stable switches which cannot occur with the same delays. Through numerical simulations, the region of complete stability of system increases with the increase of half-saturation constant, indicating that the half-saturation constant contributes to the stability of system. In addition, double Hopf bifurcations may occur due to the intersection of bifurcation curves. These results show that two different delay and half-saturation constant have important effects on the system. The numerical simulation results validate the correctness of the theoretical analyses.

Portmanteau tests have drawn much interest in economics and finance because of their strong relationship to model specification. The majority of current testing, however, concentrates on stationary time series. This article proposes an empirical likelihood-based portmanteau test for the autoregressive model, no matter if it is stationary, nearly integrated, or unit root, and with or without an intercept. It turns out that the final statistic is always asymptotically chi-squared distributed. A simulation study confirms the good finite sample performance of the proposed test before illustrating its practical merit in analyzing real data sets.

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move on G consists of taking two pebbles off one vertex and placing one on an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move, one pebble each is removed at vertices u and w that are adjacent to a vertex v, and an extra pebble is added at vertex v. The rubbling number of G, denoted by ρ(G), is the smallest number m such that for every distribution of m pebbles on G and every vertex v, at least one pebble can be moved to v by a sequence of rubbling moves. The optimal rubbling number of G, denoted by ρ_opt(G), is the smallest number k such that for some distribution of k pebbles on G, one pebble can be moved to any vertex of G. In this paper, we determine ρ(G) for a non-complete bipartite graph G ∈ B(s, t) with (delta(G)geqlceilfrac{2s+1}{3}rceil), give an upper bound of ρ(G) for G ∈ B(s, t) with (delta(G)geqlceilfrac{s+1}{2}rceil), and also obtain ρ_opt(G) for a non-complete bipartite graph G ∈ B(s, t) with (delta(G)geqlceilfrac{s+1}{2}rceil), where B(s, t) is the set of all connected bipartite graphs with partite sets of size s and t (s ≥ t) and δ(G) is the minimum degree of G.

In this paper, we consider a model which is derived from a class of the 2-dimensional Kolmogorov systems. Our purpose is to investigate the continuity of periodic solutions for this model in coefficient functions with respect to weak topologies. Finally, we provide an example as an application to Lotka-Volterra systems.

This study delves into the Hénon-type weighted elliptic equation, given by -Δ_gu = (sinh r)^α_e^u, within the context of hyperbolic space ℍⁿ, where α > 0 and n > 2. Our research reveals notable distinctions in the stability of solutions when compared to the Euclidean case.

The initial boundary value problem of a class of coupled hyperbolic systems with logarithmic source terms is considered. In this article, we classify the initial data for the global existence, finite time blow-up and long time decay of the solution. By using potential well method combined with Sobolev embedding theorem, the sufficient initial conditions of global existence, asymptotic behavior, the upper and lower bounds of blow-up time are derived at low energy level E(0) < d. These results are extended in parallel to the critical case E(0) = d. Besides, with additional assumptions on initial data, the finite time blow up result is given with arbitrary positive initial energy E(0) > 0.

We examine a quasilinear system of viscoelastic equations in this study that have fractional boundary conditions, dispersion, source, and variable-exponents. We discovered that the solution of the system is global and constrained under the right assumptions about the relaxation functions and initial conditions. After that, it is demonstrated that the blow-up has negative initial energy. Subsequently, the growth of solutions is demonstrated with positive initial energy, and the general decay result in the absence of the source term is achieved by using an integral inequality due to Komornik.

In this paper, we consider the regular s-level fractional factorial split-plot (FFSP) designs when the subplot (SP) factors are more important. The idea of general minimum lower-order confounding criterion is applied to such designs, and the general minimum lower-order confounding criterion of type SP (SP-GMC) is proposed. Using a finite projective geometric formulation, we derive explicit formulae connecting the key terms for the criterion with the complementary set. These results are applied to choose optimal FFSP designs under the SP-GMC criterion. Some two- and three-level SP-GMC FFSP designs are constructed.

In this work, we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectral problem are derived directly, and the scattering data with t = 0 are obtained accordingly to analyze the symmetry and other related properties of the Jost functions. Then we make use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel’fand-Levitan-Marchenko (GLM) integral equations. Furthermore, the time evolution of scattering data is considered, on the basis of that, the multi-soliton solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.

Given two non-empty graphs G, H and a positive integer k, the Gallai-Ramsey number gr_k(G: H) is defined as the minimum integer N such that for all n ≥ N, every exact k-edge-coloring of K_n contains either a rainbow copy of G or a monochromatic copy of H. Denote gr_k′(G: H) as the minimum integer N such that for all n ≥ N, every edge-coloring of K_n using at most k colors contains either a rainbow copy of G or a monochromatic copy of H. In this paper, we get some exact values or bounds for gr_k(P₅: H) and gr_k′(P₅: H), where H is a cycle or a book graph. In addition, our results support a conjecture of Li, Besse, Magnant, Wang and Watts in 2020.