Hopf

摘要： In this paper, a Schistosomiasis japonicum model incorporating time delay is proposed which represents the developmental time from cercaria penetration through skins of human hosts to egg laying. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equations, the local stability of the equilibria is investigated. And it proves that Hopf bifurcations occur when the time delay passes through a sequence of critical value. Furthermore, the explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using techniques from the normal form theory and Center Manifold Theorem. Some numerical simulations which support our theoretical analysis are also conducted.

摘要： In this paper Hopf bifurcation control is implemented in order to change the bifurcation from supercritical to subcritical in a differential equations system of Lorenz type. To achieve this purpose: first, a region of parameters is identified where the system has a supercritical Hopf bifurcation;second, a class of non-linear feedback control laws is proposed;finally, it is shown that there are control laws which the disturbed system undergoes subcritical Hopf bifurcation.

摘要： The repressilator is a genetic network that exhibits oscillations. The net-work is formed of three genes, each of which represses each other cyclically, creating a negative feedback loop with nonlinear interactions. In this work we present a computational bifurcation analysis of the mathematical model of the repressilator. We show that the steady state undergoes a transition from stable to unstable giving rise to a stable limit-cycle in a Hopf bifurcation. The nonlinear analysis involves a center manifold reduction on the six-dimensional system, which yields closed form expressions for the frequency and amplitude of the oscillation born at the Hopf. A parameter study then shows how the dynamics of the system are influenced for different parameter values and their associated biological significance.

摘要： This paper is concerned with the dynamics of the steady state of a two-delayed nonlinear system of functional differential equations. The stability of the steady state together with its dependence on the magnitude of time delays has been examined by means of characteristic equation corresponding to the nonlinear equation. General criteria for stability involving the two-delay equations have been obtained.

摘要： 本文对Hopf公司的6844RC型GPS卫星同步时钟的主要特点、故障判断进行了介绍，并对其在发射电台自动控制系统中的应用进行了分析。

摘要： 文章旨在构建一个以多种时间源为基础的新标准时钟系统，介绍了新系统的结构组成，以及相对应的功能，并对系统的可靠性、稳定性进行了探讨，对于取代老系统的科学性进行了阐述。

摘要： In this paper, we consider the direction and stability of time-delay induced Hopf bifurcation in a delayed predator-prey system with harvesting. We show that the positive equilibrium point is asymptotically stable in the absence of time delay, but loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold. Furthermore, using the norm form and the center manifold theory, we investigate the stability and direction of the Hopf bifurcation.

摘要： The effect of the alternative resource and time delay on conservation of forestry biomass is studied by considering a nonlinear mathematical model. In this paper, interaction between forestry biomass, industrialization pressure, toxicant pressure and technological effort is proposed and analysed. We find out the critical value of delay and observe that there is Hopf bifurcation. Using the normal form theory and the center manifold theorem, we determine the stability and direction of the bifurcating periodic solutions. Numerical simulations are given to illustrate the analytical results.

摘要： 本发明设计一种基于CPG‑Hopf网络耦合算法的水下六足机器人步态生成与转换方法，旨在解决六足机器人在运动过程中协调腿部的动作和改善步态转换时动作的顺滑度。现有的步态生成方法多数基于模型法和行为控制法，对动作的可控性不强，且不是高智能行为。基于CPG‑Hopf网络耦合振荡器是模仿动物产生的节律运动的机理，并运用到机器人的控制当中，其效果是可控性高、更稳定、运动效率更快。同时在CPG‑Hopf网络耦合振荡器的基础上优化CPG‑Hopf网络耦合算法，利用线性插值对CPG‑Hopf网络耦合算法中的关键参数进行插值解算，实现水下六足机器人在步态切换时更稳定、顺滑，从而避免了中弧形腿的关节角度发生突变，对机器人的机械与控制系统造成冲击，保证了水下六足机器人的结构安全性。

摘要： 本发明涉及一种动力系统Hopf极限环的实现方法，应用投影同步方法给出了非线性动力系统的投影同步，通过此方法可以改变动力系统的分岔性质，从而控制系统产生极限环。该方法易于实现，将在雷达、保密通信、电子对抗等领域有着广泛的应用前景及重要的实用价值。