具有性别结构的捕食者-食饵扩散模型的稳定性

讨论一类具有性别结构的捕食者-食饵扩散模型在齐次Neumann边界条件下解的存在唯一性和一致有界性,并由线性化方法和Lyapunov函数方法分别证明了该模型正平衡点的局部和全局渐近稳定.     

带有食饵保护的Gause型扩散捕食系统的稳定性分析

考虑了具有扩散项和食饵保护的Gause型捕食系统.该模型带有齐次Neumann边界条件.讨论了系统的全局吸引性以及系统非负常数平衡态的局部稳定性和全局稳定性.其条件依赖于食饵保护参数,表明了食饵保护对系统动力学行为的影响.     

一类自催化反应扩散模型正解的唯一性与稳定性

主要考虑了一类三分子自催化反应扩散系统．在齐次Dirichlet和Robin边界条件下,当反应率c适当小,系统没有共存态;当c适当大,系统至少有一个共存态;当c充分大,系统有唯一渐近稳定的共存态．特别地,在一维空间上共存态是唯一的．在齐次Neumann边界条件下系统是一个简单系统．     

一类平面拟齐次向量场的全局性质

本文利用中心投影思想证明了一类拟齐次平面向量场的几何性质仅依赖于它的诱导向量场.并根据其诱导向量场的性质证明了该向量场有10种不同拓扑结构的扇形不变区域,进而讨论了其全局拓扑结构,得到了这类向量场当n为偶数时,有17种不同的全局拓扑分类,当n为奇数时,有32种不同的全局拓扑分类.     

一类扩散的种内相食系统正平衡态的全局渐近稳定性

讨论一类扩散的种内相食的捕食者-食饵模型,该模型带有齐次Neumann边界条件.通过迭代的方法证明:在适当的条件下,该模型唯一正常数平衡解全局渐近稳定.     

带存放率的周期竞争扩散系统的稳定共存

应用上、下解方法和抛物型方程的极值原理,研究了带存放率的周期竞争系统ut-D1Δu=u（α-bu-cv）＋h,vt-D2Δv=v）d-eu-fv）＋k 在齐次Neumann边界条件下解的渐近性态,得到了该系统的全局渐近性．     

带饱和项的互惠交错扩散模型整体解的存在性和稳定性

应用能量估计方法和Gagliardo-Nirenberg型不等式证明了带饱和项的Shigesada-Kawasaki-Teramoto两种群互惠模型在齐次Neumann边值条件下整体解的存在唯一性和一致有界性.通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的条件.     

具有常数输入及非线性发生率的SIQR传染病模型

讨论一类具有常数输入及非线性发生率的SIQR传染病模型,给出了疾病是否流行的阈值R₀=1.当R₀<1时,系统的唯一无病平衡点是全局渐近稳定的;当R₀>1时,系统有两个地方病平衡点,利用特征根法讨论了这两个地方病平衡点的稳定性,得出在某些参数范围内会出现Hopf分支现象;当R₀=1时,系统有唯一的地方病平衡点,利用中心流形定理证明了该地方病平衡点是不稳定的.     

反应扩散模型的全局渐近稳定性和持续性

本文主要应用反应扩散方程的不变原理和构造适当的Liapunov泛函方法研究了一类反应扩散模型的唯一齐次正平衡态的全局渐近稳定性.进一步,根据Dunbar et al.(1986)和Hutson与Moran(1987)得出的动力学系统结果,我们得到了判别具有持续性的充分条件.     

一类带存放率的竞争扩散系统解的渐近性态

应用上、下解方法和抛物型方程的极值原理，研究了带存放率的竞争扩散系统ut-D1△u=u(a-bu-cv) h1vt-D2△v=v(d-eu-fv) k在齐次Neumann边界条件下解的渐近性态。     

Reconstructing parameters of the FitzHugh–Nagumo system from boundary potential measurements

We consider distributed parameter identification problems for the FitzHugh–Nagumo model of electrocardiology. The model describes the evolution of electrical potentials in heart tissues. The mathematical problem is to reconstruct physical parameters of the system through partial knowledge of its solutions on the boundary of the domain. We present a parallel algorithm of Newton–Krylov type that combines Newton’s method for numerical optimization with Krylov subspace solvers for the resulting Karush–Kuhn–Tucker system. We show by numerical simulations that parameter reconstruction can be performed from measurements taken on the boundary of the domain only. We discuss the effects of various model parameters on the quality of reconstructions. Action Editor: David Terman     

Interaction of noise supported Ising–Bloch fronts with Dirichlet boundaries

We investigate the behavior of fronts in bistable activator–inhibitor systems near Dirichlet boundaries. In particular, analytical and numerical investigations are performed for a FitzHugh–Nagumo dynamics. Conditions for a bound state and for a rebound of fronts are formulated. We also show fronts which oscillate between two reflecting boundaries. If additive noise is applied, nucleation of pairwise fronts near the boundary is observed. The front running towards the boundary is reflected there, and a pulse-like sequence of fronts propagating away from the boundary is established. Thus, noise and the boundary play the role of a pacemaker of a permanent progression of fronts. The sequence becomes highly ordered at optimal noise level. We also present examples of a two dimensional generalization of this noisy pacemaker.     

Symmetric bursting behaviors in the generalized FitzHugh–Nagumo model

In the current paper, we have investigated the generalized FitzHugh–Nagumo model. We have shown that symmetric bursting behaviors of different types could be observed in this model with an appropriate recovery term. A modified version of this system is used to construct bursting activities. Furthermore, we have shown some numerical examples of delayed Hopf bifurcation and canard phenomenon in the symmetric bursting of super-Hopf/homoclinic type near its super-Hopf and homoclinic bifurcations, respectively.     

Weak periodic signal detection by sine-Wiener-noise-induced resonance in the FitzHugh–Nagumo neuron

Based on the FitzHugh–Nagumo (FHN) neuron model subjected to sine-Wiener (SW) noise, impacts of SW noise on weak periodic signal detection are investigated by calculating response measure Q for characterizing synchronization between the input signal and the output temporal activities of the neuron. It is numerically demonstrated that the response measure Q can achieve the optimal value under appropriate and moderate intensity or correlation time of SW noise, suggesting the occurrence of SW-noise-induced stochastic resonance. Furthermore, the optimal value of Q is sensitive to correlation time. Consequently, the correlation time of SW noise has a great influence on the performance of signal detection in the FHN neuron.     

A molecular dynamics boundary condition for heat exchange between walls and a fluid

In molecular dynamics simulations of heat transfer in micro channels, a lot of computation time is used when the wall molecules are explicitly simulated. To save computation time, implicit boundary conditions, such as the Maxwell conditions, can be used. With these boundary conditions, heat transfer is still a problem. In this work, we derive a new boundary condition based on a vibrating potential wall. The heat-transfer properties of the new boundary condition are shown to be comparable with those of the explicit wall. The computation time needed for the implicit boundary condition is very small compared with that needed for the explicit simulation.     

The Chapman-Enskog procedure for an age-structured population model: initial, boundary and corner layer corrections

We consider a mathematical model of an age-structured population of some fisheries (for example, anchovies, sardines or soles). Two time scales are involved in the problem: the fast time scale for the migration dynamics and the slow time scale for the demographic process. At a first step, we study the so called 'aggregated' system by means of the semigroups theory. Then, we study the asymptotic behaviour of the model by using the Chapman-Enskog procedure. In particular, we study initial, boundary and corner layer effects in order to obtain the exact initial and boundary conditions the approximated solution has to satisfy.     

Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries

The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream domains with 3D numerical models of the upstream vasculature. This prior work either included pure resistance boundary conditions or impedance boundary conditions based on assumed periodicity of the solution. However, flow and pressure in arteries are not necessarily periodic in time due to heart rate variability, respiration, complex transitional flow or acute physiological changes. We present herein an approach for prescribing lumped parameter outflow boundary conditions that accommodate transient phenomena. We have applied this method to compute haemodynamic quantities in different physiologically relevant cardiovascular models, including patient-specific examples, to study non-periodic flow phenomena often observed in normal subjects and in patients with acquired or congenital cardiovascular disease. The relevance of using boundary conditions that accommodate transient phenomena compared with boundary conditions that assume periodicity of the solution is discussed.     

Asymptotics of Conduction Velocity Restitution in Models of Electrical Excitation in the Heart

We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh–Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified “caricature” of Noble (J. Physiol. Lond. 160:317–352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177–210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler–Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method.     

Respiratory sinus arrhythmia as a second order system

The presented study describes the influence of respiration on heart rate, under controlled respiration conditions. In addition, this study makes a comparison of a simple physical model, the spring-mass system, with the biophysics of respiration. It is possible to use the equations describing the behaviour of the respiratory system, under certain conditions, and analyse them in a way similar to the equations that describe the physical spring-mass system. The results of the heart rate and respiration measurements effected on 10 subjects at various respiration frequencies show us that the heart rate behaves as a second order system within the boundary conditions during a longer period of constant respiration. The results also show that the heart rate behaves as a second order system within the intermediate mode during short time intervals when there is no respiration.