Showing papers by "Patricia J. Y. Wong published in 2014"
TL;DR: In this article, a class of periodic discrete spline interpolates in one and two independent variables was developed, and explicit error bounds were derived for the periodic quintic and biquintic discrete splines interpolates.
10 citations
TL;DR: This paper uses discrete cubic spline based on central differences to obtain approximate solution of a second-order boundary value problem and shows that the method is of order 4 if a parameter takes a specific value, else it is of orders of order 2.
Abstract: In this paper, we use discrete cubic spline based on central differences to obtain approximate solution of a second-order boundary value problem. It is shown that the method is of order 4 if a parameter takes a specific value, else it is of order 2. Two numerical examples are included to illustrate our method as well as to compare the performance with other numerical methods proposed in the literature.
10 citations
TL;DR: In this article, the authors studied the periodicity and global asymptotic stability of a generalized Lotka-Volterra's competition system with delays and established sufficient conditions for the existence and stability of periodic solution of such nonlinear differential equations.
Abstract: The main purpose of this paper is to study the periodicity and global asymptotic stability of a generalized Lotka-Volterra’s competition system with delays. Some sufficient conditions are established for the existence and stability of periodic solution of such nonlinear differential equations. The approaches are based on Mawhin’s coincidence degree theory, matrix spectral theory, and Lyapunov functional.
10 citations
TL;DR: The relationship between college students’ VPA and alcohol consumption and between MPA and cigarette smoking is similar across the East Asian economies, whereas the relationship between Vpa and smoking varies substantially.
Abstract: Objective:To identify levels of moderate-intensity physical activity (MPA) and vigorous-intensity physical activity (VPA) in a representative sample of college students in six East Asian economies and examine their relationship with weight, alcohol consumption and cigarette smoking.Design:Cross-sectional survey.Setting:College students recruited from 21 different colleges in six East Asian economies.Method:Self-reported physical activity, weight, height, alcohol consumption, and smoking were assessed using already-validated instruments. Multiple logistic regression models of MPA and VPA were separately performed for each economy, controlling for age, gender, living area before college, military experience, paid employment, and religion. All the analyses were performed using SAS 9.2 with clustering effects accounted for.Results:Being a heavy drinker increased the odds of engaging in VPA in five economies (adjusted odds ratio [AOR] = 1.56 to 2.65). Cigarette smoking was not associated with MPA in any econom...
9 citations
TL;DR: In this article, the complementary Lidstone boundary value problem is considered, where the nonlinear term F depends on y and this derivative dependence is seldom investigated in the literature and a new technique is required to tackle the problem.
Abstract: We consider the following complementary Lidstone boundary value problem: (-1) m y (2m+1) (t )= F(t, y(t), y � (t)), t ∈ (0, 1), y(0) = 0, y (2k-1) (0) = y (2k-1) (1) = 0, 1 ≤ k ≤ m. By using fixed point theorems of Leggett-Williams and Avery, we offer several criteria for the existence of three positive solutions of the boundary value problem. Examples are also included to illustrate the results obtained. We note that the nonlinear term F depends on yand this derivative dependence is seldom investigated in the literature and a new technique is required to tackle the problem. MSC: 34B15; 34B18
8 citations
TL;DR: In this paper, the authors used deficient discrete cubic spline to obtain approximate solution of a system of second-order boundary value problems, and they showed that the method is of order 2 when a parameter takes a specific value.
Abstract: In this paper we use deficient discrete cubic spline to obtain approximate solution of a system of second order boundary value problems. It is shown that the method is of order 2 when a parameter takes a specific value. A well known numerical example is presented to illustrate our method as well as to compare the performance with other numerical methods proposed in the literature.
6 citations
TL;DR: In this article, it was shown that if the nonlinear term is bounded, the perturbed non-autonomous system with non-uniform exponential dichotomy has a unique solution.
Abstract: Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies . However, this condition is very restricted. There are few functions satisfying . In some sense, this assumption is not reasonable enough. More suitable assumption should be . To the best of the authors' knowledge, there is no paper considering the existence and uniqueness of solution to the perturbed nonautonomous system with a relatively conservative assumption . In this paper, we prove that if the nonlinear term is bounded, the perturbed nonautonomous system with nonuniform exponential dichotomy has a unique solution. The technique employed to prove Theorem 4 is the highlight of this paper.
6 citations
TL;DR: In this article, Barreira and Valls proved that the nonlinear impulsive system is topologically conjugated to its linear system under some suitable conditions, under the assumption that the linear system has a nonuniform exponential dichotomy.
Abstract: This paper gives a version of Hartman-Grobman theorem for the impulsive differential equations. We assume that the linear impulsive system has a nonuniform exponential dichotomy. Under some suitable conditions, we proved that the nonlinear impulsive system is topologically conjugated to its linear system. Indeed, we do construct the topologically equivalent function (the transformation). Moreover, the method to prove the topological conjugacy is quite different from those in previous works (e.g., see Barreira and Valls, 2006).
5 citations
TL;DR: In this article, it was shown that the non-linear elltic equation involving the generalized -Laplacian operator with Neumann boundary conditions has a unique solution in, which is the zero point of a suitably defined nonlinear m-accretive mapping.
Abstract: In this paper, we first prove some perturbation results on the ranges of maximal monotone operators, one of which is then used to show that the non-linear elltic equation involving the generalized -Laplacian operator with Neumann boundary conditions has a unique solution in . This unique solution is shown to be the zero point of a suitably defined non-linear m-accretive mapping. Finally, two kinds of iterative sequences are constructed and proved to converge strongly and weakly to the unique solution, respectively. Some new techniques of constructing appropriate operators and decomposing the equations are employed, which extend and complement some of the previous work.
5 citations
TL;DR: In this paper, it was shown that when the linear impulsive system has ordinary dichotomy, the nonlinear system is topologically conjugated to,,,,, where,, represents the jump of the solution at.
Abstract: This paper presents a linearization theorem for the impulsive differential equations when the linear system has ordinary dichotomy. We prove that when the linear impulsive system has ordinary dichotomy, the nonlinear system , , , , is topologically conjugated to , , , , where , , represents the jump of the solution at . Finally, two examples are given to show the feasibility of our results.
3 citations
TL;DR: In this article, sufficient conditions are obtained for the existence of at least two positive periodic solutions for a plant-hare model with toxin-determined biochemical response (non-monotone).
Abstract: Based on Mawhin's coincidence degree theory, sufficient conditions are obtained for the
existence of at least two positive periodic solutions for a plant-hare model with toxin-determined
functional response (nonmonotone). Some new technique is used in this paper, because standard
arguments in the literature are not applicable.
TL;DR: In this article, two discrete predator-prey models in patchy environment, one without dispersal corridors and one with a dispersal corridor, were compared and it was found that the dispersion of the prey from one patch to another is helpful to the permanence of the predator.
Abstract: We study two discrete predator-prey models in patchy environment, one without dispersal corridors and one with dispersal corridors. Dispersal corridors are passes that allow the migration of species from one patch to another and their existence may influence the permanence of the model. We will offer sufficient conditions to guarantee the permanence of the two predator-prey models. By comparing the two permanence criteria, we discuss the effects of dispersal corridors on the permanence of the predator-prey model. It is found that the dispersion of the prey from one patch to another is helpful to the permanence of the prey if the population growth of the prey is density dependent; however, this dispersion of the prey could be disadvantageous or advantageous to the permanence of the predator. Five numerical examples are presented to confirm the theoretical results obtained and to illustrate the effects of dispersal corridors on the permanence of the predator-prey model.
TL;DR: In this paper, the existence of homoclinic solutions for non-autonomous singular Hamiltonian systems was shown for the case that the potential has a singularity at, and the gradient of the gradient at.
Abstract: We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems , (HS) where , , is a continuous bounded function, and the potential has a singularity at , and is the gradient of at . The novelty of this paper is that, for the case that and (HS) is nonautonomous (neither periodic nor almost periodic), we show that (HS) possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum of . Different from the cases that (HS) is autonomous or (HS) is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS) is nonautonomous and . Besides the usual conditions on , we need the assumption that for all to guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.
TL;DR: In this article, the authors obtain sufficient conditions for the global existence of multiple positive periodic solutions of a delayed stage-structured plant-hare model with a toxin-determined functional response.
Abstract: The purpose of this paper is to obtain some sufficient conditions for the global existence of multiple positive periodic solutions of a delayed stage-structured plant-hare model with a toxin-determined functional response. Some novel estimation techniques to construct two open subsets for a priori bounds are employed.
TL;DR: In this paper, the existence and uniqueness of positive solutions for a class of singular m-point boundary value problems of second order differential equations on a measure chain was studied. And the maximal principle theorem was used to obtain a sufficient condition for the existence of both positive and negative solutions.
Abstract: We study the existence and uniqueness of positive solutions for a class of singular m-point boundary value problems of second order differential equations on a measure chain. A sharper sufficient condition for the existence and uniqueness of positive solutions as well as positive solutions is obtained by the technique of lower and upper solutions and the maximal principle theorem.
01 Dec 2014
TL;DR: It is found that the effects of prey dispersal on the permanence of the predator-prey model are two-fold.
Abstract: We study two discrete predator-prey models in patchy environment, one without dispersal corridors and one with dispersal corridors for the prey. Sufficient conditions to guarantee the permanence of the two predator-prey models are given. By comparing the two permanence criteria, we find that the effects of prey dispersal on the permanence of the predator-prey model are two-fold. Numerical examples are presented to illustrate the effects of the dispersion on the permanence of the predator-prey model.