• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.749-756
• /
• 2013

In this paper, we consider a diffusive delayed predator-prey model with Beddington-DeAngelis type functional response under homogeneous Neumann boundary conditions, where the discrete time delay covers the period from the birth of immature preys to their maturity. We investigate the global existence of nonnegative solutions and the long-term behavior of the time-dependent solution of the model.

• Kyungpook Mathematical Journal
• /
• v.50 no.2
• /
• pp.255-266
• /
• 2010

We consider a delayed predator-prey system with Holling II functional response. Firstly, the paper considers the stability and local Hopf bifurcation for a delayed prey-predator model using the basic theorem on zeros of general transcendental function, which was established by Cook etc.. Secondly, special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations supporting the theoretical analysis are given.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.147-159
• /
• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

• Animal Systematics, Evolution and Diversity
• /
• v.30 no.1
• /
• pp.39-43
• /
• 2014

In this brief report, alternative time-varying diversification rate models were fitted onto the phylogeny of global amphibians by considering one-constant-rate (OCR), one-continuous-shift (OCS) and multiple-discrete- shifts (MDS) situations. The OCS diversification model was rejected by ${\gamma}$ statistic (${\gamma}=-5.556$, p<0.001), implying the existence of shifting diversification rates for global amphibian phylogeny. Through model selection, MDS diversification model outperformed OCS and OCR models using "laser" package under R environment. Moreover, MDS models, implemented using another R package "MEDUSA", indicated that there were sixteen shifts over the internal nodes for amphibian phylogeny. Conclusively, both OCS and MDS models are recommended to compare so as to better quantify rate-shifting trends of species diversification. MDS diversification models should be preferential for large phylogenies using "MEDUSA" package in which any arbitrary numbers of shifts are allowed to model.

• The Pure and Applied Mathematics
• /
• v.24 no.4
• /
• pp.201-209
• /
• 2017

We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-specific competition pressures and the inter-specific cooperative pressures dominated by intra-specific competition pressures. Under these conditions the $W^1_2-bound$ and the time global existence of the solution for the cooperative cross-diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.

• Journal of the Korean Mathematical Society
• /
• v.60 no.3
• /
• pp.565-586
• /
• 2023

We study the Dirichlet problem for the degenerate nonlocal parabolic equation u_t - a(||∇u||²_L²(Ω))∆u = C_b ||u||^β_L²(Ω) |u|^q(x,t)-2 u log |u| + f in Q_T, where Q_T := Ω × (0, T), T > 0, Ω ⊂ ℝ^N, N ≥ 2, is a bounded domain with a sufficiently smooth boundary, q(x, t) is a measurable function in Q_T with values in an interval [q^-, q⁺] ⊂ (1, ∞) and the diffusion coefficient a(·) is a continuous function defined on ℝ₊. It is assumed that a(s) → 0 or a(s) → ∞ as s → 0⁺, therefore the equation degenerates or becomes singular as ||∇u(t)||2 → 0. For both cases, we show that under appropriate conditions on a, β, q, f the problem has a global in time strong solution which possesses the following global regularity property: ∆u ∈ L²(Q_T) and a(||∇u||²_L²(Ω))∆u ∈ L²(Q_T ).

• Honam Mathematical Journal
• /
• v.45 no.1
• /
• pp.54-70
• /
• 2023

In this article, we state and prove several new retarded nonlinear integral and integro-differential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Applications are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.11 no.4
• /
• pp.116-123
• /
• 2008

In this paper we study the performance of the measurement time-delay estimation of tightly-coupled GPS/INS(Global positioning system/Inertial Navigation system) system. Generally, the heading error estimation performance of loosely-coupled GPS/INS system using GPS's Navigation Solution is poor. In the case of tightly-coupled GPS/INS system using pseudo-range and pseudo-range rate, the heading error estimation performance is better. However, the time-delay error on the measurement(pseudo-range rate) make the heading error estimation performance degraded. So that, we propose the time-delay model on the measurement and compose the time-delay estimator. And we confirm that the heading error estimation performance in the case of measurement time-delay existence is similar with the case of no-delay by Monte-Carlo simulation.

• Journal of applied mathematics & informatics
• /
• v.29 no.5_6
• /
• pp.1381-1393
• /
• 2011

In this paper, we consider two-species periodic Gilpin-Ayala competition system with delay and impulsive effect. By using some analysis methods, sufficient conditions for the permanence of the system are derived. Further, we give the conditions of the existence and global asymptotic stable of positive periodic solution.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1195-1219
• /
• 2017

In this paper, the limit behavior of solution for the $Schr{\ddot{o}}dinger$ equation with random dispersion and time-dependent nonlinear loss/gain: $idu+{\frac{1}{{\varepsilon}}}m({\frac{t}{{\varepsilon}^2}}){\partial}_{xx}udt+{\mid}u{\mid}^{2{\sigma}}udt+i{\varepsilon}a(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$ is studied. Combining stochastic Strichartz-type estimates with $L^2$ norm estimates, we first derive the global existence for $L^2$ and $H^1$ solution of the stochastic $Schr{\ddot{o}}dinger$ equation with white noise dispersion and time-dependent loss/gain: $idu+{\Delta}u{\circ}d{\beta}+{\mid}u{\mid}^{2{\sigma}}udt+ia(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as ${\varepsilon}{\rightarrow}0$ in one-dimensional $L^2$ subcritical and critical cases.