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81.
We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota–Baxter operators, e.g. the Riemann integral map or Jackson's q-integral. 相似文献
82.
83.
To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic. 相似文献
84.
ALONSO LVAREZ Jos Nicanor FERNNDEZ VILABOA Jos Manuel GONZLEZ RODRíIGUEZ Ramón SONEIRA CALVO Carlos 《中国科学 数学(英文版)》2011,(5)
In this paper we study the projections of weak braided Hopf algebras using the notion of Yetter-Drinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study ofthe structure of weak Hopf algebras with a projection in a braiding setting obtaining a categorical equivalencebetween the category of weak Hopf algebra projections associated with a weak Hopf algebra H living in abraided monoidal category and the category of Hopf algebras in the non-strict braided monoidal cate... 相似文献
85.
Noise-induced synchronous stochastic oscillations small scale cultured heart-cell networks
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Yuan Lan Liu Zhi-Qiang Zhang Hui-Min Ding Xue-Li Yang Ming-Hao Gu Hua-Guang Ren Wei 《中国物理 B》2011,(2):133-147
This paper reports that the synchronous integer multiple oscillations of heart-cell networks or clusters are observed in the biology experiment. The behaviour of the integer multiple rhythm is a transition between super- and sub- threshold oscillations, the stochastic mechanism of the transition is identified. The similar synchronized oscillations are theoretically reproduced in the stochastic network composed of heterogeneous cells whose behaviours are chosen as excitable or oscillatory states near a Hopf bifurcation point. The parameter regions of coupling strength and noise density that the complex oscillatory rhythms can be simulated are identified. The results show that the rhythm results from a simple stochastic alternating process between super- and sub-threshold oscillations. Studies on single heart cells forming these clusters reveal excitable or oscillatory state nearby a Hopf bifurcation point underpinning the stochastic alternation. In discussion, the results are related to some abnormal heartbeat rhythms such as the sinus arrest. 相似文献
86.
Cas van der AvoortRein van der Hout Joost Hulshof 《Physica D: Nonlinear Phenomena》2011,240(11):913-919
We study the response of a MEMS resonator, driven in an in-plane length-extensional mode of excitation. It is observed that the amplitude of the resulting vibration has an upper bound, i.e., the response shows saturation. We present a model for this phenomenon, incorporating interaction with a bending mode. We show that this model accurately describes the observed phenomena. The in-plane (“trivial”) mode is shown to be stable up to a critical value of the amplitude of the excitation. At this value, a new “bending” branch of solutions bifurcates. For appropriate values of the parameters, a subsequent Hopf bifurcation causes a beating phenomenon, in accordance with experimental observations. 相似文献
87.
Yan Wang Fred Brauer Jianhong Wu Jane M. Heffernan 《Journal of Mathematical Analysis and Applications》2014
The use of combination antiretroviral therapy has proven remarkably effective in controlling HIV disease progression and prolonging survival. However, the emergence of drug resistance can occur. It is necessary that we gain a greater understanding of the evolution of drug resistance. Here, we consider an HIV viral dynamical model with general form of target cell density, drug resistance and intracellular delay incorporating antiretroviral therapy. The model includes two strains: wild-type and drug-resistant. The basic reproductive ratio for each strain is obtained for the existence of steady states. Qualitative analysis of the model such as the well-posedness of the solutions and the equilibrium stability is provided. Global asymptotic stability of the disease-free and drug-resistant steady states is shown by constructing Lyapunov functions. Furthermore, sufficient conditions related to the properties of the target cell density are obtained for the local asymptotic stability of the positive steady state. Numerical simulations are conducted to study the impact of target cell density and intracellular delay focusing on the stability of the positive steady state. The occurrence of Hopf bifurcation of periodic solutions is shown to depend on the target cell density. 相似文献
88.
89.
In this paper, we consider a generalized model of the two friction models, both of which have two different types of control forces with time-delayed feedback proposed by Ashesh Sara et al. By taking the time delay as the bifurcation parameter, we discuss the local stability of the Hopf bifurcations. Under some condition, the generalized model harbors a phenomenon that the equilibrium may undergo finite switches from stability to instability to stability and finally become unstable. By applying the method introduced by Faria and Magalhaes, we compute the normal form on the center manifold to determine the direction and stability of the Hopf bifurcations. Numerical simulations are carried out and more than one periodic solutions may exist according to the bifurcation diagram given by BIFTOOL. Finally a brief conclusion is presented. 相似文献
90.
Jiangbin Chen 《Annals of Differential Equations》2014,(4):386-393
A predator-prey system with Holling-IV functional response is investigated. It is shown that the system has a positive equilibrium, which is a cusp of co-dimension 2 under certain conditions. When the parameters vary in a small neighborhood of the values of parameters, the model undergoes the Bogdanov-Takens bifurcation. Dif- ferent kinds of bifurcation phenomena are exhibited, which include the saddle-node bifurcation, the Hopf bifurcation and the homo-clinic bifurcation. Some computer simulations are presented to illustrate the conclusions. 相似文献