耦合Hodgkin-Huxley方程中同相解的稳定性

本文证明了耦合Ｈｏｄｇｋｉｎ－Ｈｕｘｌｅｙ方程中同相解的稳定性．     

Poincaré方程的线性差耦合系统

该文对Poincare方程的线性差耦合系统的同相解及反相解进行研究,得到了同相解稳定的参数区域,并在对角线性差耦合的情形下.对其反相解的存在性及稳定性进行了完整的分析,改进了文[1]的结果.     

双水槽耦合孤波观察及其理论分析 *

最新实验发现,当两水槽底部连通构成耦合双槽时,这个耦合系统就支持一对同相或反相的耦合孤波.描述了这种耦合孤波对的动力学特性,包括处于不同槽中孤波间的相互作用.给出了支配这一过程的孤波耦合方程组,并由此给出了初步的理论解释,即几种稳态耦合孤波解.     

一类高次自催化耦合反应扩散系统的分歧和斑图

考虑了一类由于自催化剂的耦合而发生的反应扩散系统的空间结构．利用线性化理论讨论了平衡态解的稳定性并且证明了在非耦合系统中空间非一致解出现分歧的必要条件．进一步,利用弱非线性理论讨论了分歧点并且给出了弱耦合系统的图灵分歧解的振幅方程及其性质．     

一类耦合非线性波方程的行波解分支

利用动力系统的Hopf分支理论来研究耦合非线性波方程周期行波解的存在性和稳定性．应用行波法把一类耦合非线性波方程转换为三维动力系统来研究,从而给在不同的参数条件下给出了周期解存在和稳定性的充分条件．     

耦合BBM方程组孤立波解的轨道稳定性(英文)

本文研究具有Hamilton形式的耦合BBM方程组孤立波解的轨道稳定性.首先找到两族显式孤立波解.然后通过详细的谱分析证明出孤立波解的轨道稳定性.     

一类微气泡耦合时滞系统的周期解

研究一类微气泡耦合时滞系统的稳定性以及Hopf分支,得到了稳定性和Hopf分支出现的条件,并利用泛函微分方程相关理论讨论出分支周期解的分支方向、稳定性和分支周期的变化律.     

拟线性双曲抛物耦合组的激波解及高维等温辐射激波解的线性稳定性

本文讨论双曲抛物耦合守恒律组的激波解的一致稳定性,证明了伴随线性化问题的能量估计及存在性,由此并可得非线性问题解的存在性.对等温辐射激波,稳定性等价于Lax的等温音速激波不等式.     

一类具扩散的Ivlev型捕食模型

研究一类具有扩散的Ivlev型捕食模型.首先利用线性化和特征值法给出正平衡解在常微分系统和加入自扩散的弱耦合偏微分系统下的局部渐近稳定性,其次,讨论在加入交错扩散的强耦合系统下会引起平衡解的Turing不稳定,最后给出数值模拟验证理论结果.     

一类耗散型电流体动力学方程组自相似解的渐近稳定性

主要考虑一类来源于电流体动力学中的由非线性非局部方程组耦合而成的耗散型系统的初值问题.利用Lorentz空间中广义L~p-L~q热半群估计和广义Hardy-Littlewood-Sobolev不等式,首先证明了该系统在Lorentz空间中自相似解的整体存在性和唯一性,然后建立了自相似解当时间趋于无穷时的渐近稳定性.因为Lorentz空间包含了具有奇性的齐次函数,因次上述结果保证了具有奇性的初值所对应的自相似解的整体存在性和渐近稳定性.     

Nonexistence theorem except the out-of-phase and in-phase solutions in the coupled van der Pol equation system

We consider a coupled van der Pol equation system. Our coupled system consists of two van der Pol equations that are connected with each other by linear terms. We assume that two distinctive solutions (out-of-phase and in-phase solutions) exist in the dynamical system of coupled equations and give answers to some problems.     

Dynamics of a model of two delay-coupled relaxation oscillators

This paper investigates the dynamics of a new model of two coupled relaxation oscillators. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach with jumps. Existence, bifurcation and stability of in-phase periodic motions is studied. Simple periodic motions, which involve exactly two jumps per period, are found to have large plateaus in parameter space. These plateaus are separated by regions of complicated dynamics, reminiscent of the Devil’s Staircase. Stability of motions in the in-phase manifold are contrasted with stability of motions in the full phase space.     

Synchronization of time-delay coupled pulse oscillators

We present a detailed study of the dynamics of pulse oscillators with time-delayed coupling. We get the return maps, obtain strict solutions and analyze their stability. For the case of two oscillators, a periodical structure of synchronization regions is found in parameter space, and the regions corresponding to in-phase and antiphase regimes alternate with growth of time delay. Two types of switching between in-phase and antiphase regimes are studied. We also show that for different parameters coupling delay may have synchronizing or desynchronizing effect. Another novel result is that phase locked regimes exist for arbitrary large values. The specificity of system dynamics with large delay is studied.     

Symmetry breaking, coupling management, and localized modes in dual-core discrete nonlinear-Schrödinger lattices

We introduce a system of two linearly coupled discrete nonlinear Schrödinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose-Einstein condensates (BEC). Using an averaging procedure based on the multiscale method, we derive a system of averaged (autonomous) equations, which take the form of coupled DNLSEs with additional nonlinear coupling terms of the four-wave-mixing type. We identify stability regions for fundamental onsite discrete symmetric solitons (single-site modes with equal norms in both components), as well as for two-site in-phase and twisted modes, the in-phase ones being completely unstable. The symmetry-breaking bifurcation, which destabilizes the fundamental symmetric solitons and gives rise to their asymmetric counterparts, is investigated too. It is demonstrated that the averaged equations provide a good approximation in all the cases. In particular, the symmetry-breaking bifurcation, which is of the pitchfork type in the framework of the averaged equations, corresponds to a Hopf bifurcation in terms of the original system.     

Bistability of rotational modes in a system of coupled pendulums

The main goal of this research is to examine any peculiarities and special modes observed in the dynamics of a system of two nonlinearly coupled pendulums. In addition to steady states, an in-phase rotation limit cycle is proved to exist in the system with both damping and constant external force. This rotation mode is numerically shown to become unstable for certain values of the coupling strength. We also present an asymptotic theory developed for an infinitely small dissipation, which explains why the in-phase rotation limit cycle loses its stability. Boundaries of the instability domain mentioned above are found analytically. As a result of numerical studies, a whole range of the coupling parameter values is found for the case where the system has more than one rotation limit cycle. There exist not only a stable in-phase cycle, but also two out-of phase ones: a stable rotation limit cycle and an unstable one. Bistability of the limit periodic mode is, therefore, established for the system of two nonlinearly coupled pendulums. Bifurcations that lead to the appearance and disappearance of the out-ofphase limit regimes are discussed as well.     

Bifurcation analysis of a simple 3D oscillator and chaos synchronization of its coupled systems

Tama?evi?ius et al. proposed a simple 3D chaotic oscillator for educational purpose. In fact the oscillator can be implemented very easily and it shows typical bifurcation scenario so that it is a suitable training object for introductory education for students. However, as far as we know, no concrete studies on bifurcations or applications on this oscillator have been investigated. In this paper, we make a thorough investigation on local bifurcations of periodic solutions in this oscillator by using a shooting method. Based on results of the analysis, we study chaos synchronization phenomena in diffusively coupled oscillators. Both bifurcation sets of periodic solutions and parameter regions of in-phase synchronized solutions are revealed. An experimental laboratory of chaos synchronization is also demonstrated.     

Quantification of synchronization phenomena in two reciprocally gap-junction coupled bursting pancreatic β-cells

This paper aims to discuss our research into synchronized transitions in two reciprocally gap-junction coupled bursting pancreatic β-cells. Numerical results revealed that propagations of synchronous states could be induced not only by changing the coupling strength, but also by varying the slow time constant. Firstly, these asynchronous and synchronous states such as out-of-phase, almost in-phase and in-phase synchronization were specifically demonstrated by phase portraits and time evolutions. By comparing interspike intervals (ISI) bifurcation diagrams of two coupled neurons with an individual neuron, we found that coupling strength played a critical role in tonic-to-bursting transitions. In particular, with the phase difference and ISI-distance being introduced, regions of various synchronous and asynchronous states were plotted in a two-dimensional parameter space. More interestingly, it was found that the coupled neurons could always realize complete synchronization as long as the coupling strength was appropriate.