Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of ...Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.展开更多
The two point boundary value problem(BVP) with general boundary value conditions in Banach spaces is considered. Using the Green function of the two point BVP on R 1 and beginning at its upper solution v 0 and the...The two point boundary value problem(BVP) with general boundary value conditions in Banach spaces is considered. Using the Green function of the two point BVP on R 1 and beginning at its upper solution v 0 and then at its lower solution u 0, monotone iterative sequences are constructed in ordered interval [u 0, v 0] and it is proved that the sequences converge to their maximal and minimal solutions, respectively. Moreover, it is shown that the sequence, as above, converges to the unique solution of the BVP for any initial value on the ordered interval [u 0, v 0]. Also, the error estimate of the solution's converging sequence is given.展开更多
The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the ...The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns.The parametric vibration equation is established for the test model using the finite-element method.The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method.The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model.Compared with the experiment,the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena,and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones.For a continuous beam bridge,when the ratio of multipoint excitation frequency(applied to the columns)to natural frequency of the continuous girder is approximately equal to 2,the continuous beam may undergo a strong auto-parametric resonance.Combined with the present experiment and analysis,a hypothesis of Volgograd Bridge's serpentine vibration is discussed.展开更多
针对旋转倒立摆自动起摆的控制问题,提出了基于BVP算法的自动起摆控制策略。该方法将倒立摆起摆控制问题转化成求解非线性方程的两点边值问题(Two-point BoundaryValue Problem BVP),构造了含参变量具有傅立叶级数形式的起摆力矩函数,...针对旋转倒立摆自动起摆的控制问题,提出了基于BVP算法的自动起摆控制策略。该方法将倒立摆起摆控制问题转化成求解非线性方程的两点边值问题(Two-point BoundaryValue Problem BVP),构造了含参变量具有傅立叶级数形式的起摆力矩函数,将力矩函数代入倒立摆系统,利用Matlab工具箱中的bvp4c函数求解两点边值条件,获得起摆过程的起摆控制的时间序列。基于BVP算法的起摆控制的求解,本质上属于开环前馈控制。为了抑制参数摄动,进行了平衡点附近的稳摆控制设计。稳摆设计是针对系统模型不稳定性和非最小相位特性分别进行的。对起摆、稳摆及其切换过程进行了仿真和实验研究,验证了所提出的自动起摆控制策略的有效性。展开更多
本文运用数值计算的方法研究了包含周期刺激项Acos(ω_0t)的BVP(Bonhoeffer-van der Pol)模型随控制参数ω_0变化出现的分岔、混沌和阵发混沌.结果表明,受环境周期性变化的影响,在适当的条件下,一类可兴奋细胞系统表现出的复杂的电生理...本文运用数值计算的方法研究了包含周期刺激项Acos(ω_0t)的BVP(Bonhoeffer-van der Pol)模型随控制参数ω_0变化出现的分岔、混沌和阵发混沌.结果表明,受环境周期性变化的影响,在适当的条件下,一类可兴奋细胞系统表现出的复杂的电生理活动是与混沌行为密切相关的.展开更多
The existence of positive solutions to second-order periodic BVPs-u'+Mu =j(t, u),t(0) = u(2π),u'(0) = '(2π) and u'+ Mu = I(t, u), u(0) = u(2π), u'(0) = u'(2π)is proved by a simple appliCati...The existence of positive solutions to second-order periodic BVPs-u'+Mu =j(t, u),t(0) = u(2π),u'(0) = '(2π) and u'+ Mu = I(t, u), u(0) = u(2π), u'(0) = u'(2π)is proved by a simple appliCation of a Fixed point Theorem in cones due to Krasnoselskii.展开更多
The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and se...The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.展开更多
We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system.By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order...We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system.By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency.Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples,in which different types of bursting oscillations such as sub Hopf/sub Hopf burster, sub Hopf/fold-cycle burster, and doublefold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states（QSs） and the repetitive spiking states（SPs） may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically.展开更多
文摘Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.
文摘The two point boundary value problem(BVP) with general boundary value conditions in Banach spaces is considered. Using the Green function of the two point BVP on R 1 and beginning at its upper solution v 0 and then at its lower solution u 0, monotone iterative sequences are constructed in ordered interval [u 0, v 0] and it is proved that the sequences converge to their maximal and minimal solutions, respectively. Moreover, it is shown that the sequence, as above, converges to the unique solution of the BVP for any initial value on the ordered interval [u 0, v 0]. Also, the error estimate of the solution's converging sequence is given.
基金National Natural Science Foundation of China under Grant No.51879191。
文摘The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns.The parametric vibration equation is established for the test model using the finite-element method.The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method.The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model.Compared with the experiment,the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena,and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones.For a continuous beam bridge,when the ratio of multipoint excitation frequency(applied to the columns)to natural frequency of the continuous girder is approximately equal to 2,the continuous beam may undergo a strong auto-parametric resonance.Combined with the present experiment and analysis,a hypothesis of Volgograd Bridge's serpentine vibration is discussed.
文摘针对旋转倒立摆自动起摆的控制问题,提出了基于BVP算法的自动起摆控制策略。该方法将倒立摆起摆控制问题转化成求解非线性方程的两点边值问题(Two-point BoundaryValue Problem BVP),构造了含参变量具有傅立叶级数形式的起摆力矩函数,将力矩函数代入倒立摆系统,利用Matlab工具箱中的bvp4c函数求解两点边值条件,获得起摆过程的起摆控制的时间序列。基于BVP算法的起摆控制的求解,本质上属于开环前馈控制。为了抑制参数摄动,进行了平衡点附近的稳摆控制设计。稳摆设计是针对系统模型不稳定性和非最小相位特性分别进行的。对起摆、稳摆及其切换过程进行了仿真和实验研究,验证了所提出的自动起摆控制策略的有效性。
文摘The existence of positive solutions to second-order periodic BVPs-u'+Mu =j(t, u),t(0) = u(2π),u'(0) = '(2π) and u'+ Mu = I(t, u), u(0) = u(2π), u'(0) = u'(2π)is proved by a simple appliCation of a Fixed point Theorem in cones due to Krasnoselskii.
文摘The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.
基金Project supported by the National Natural Science Foundation of China(Grant No.21276115)
文摘We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system.By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency.Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples,in which different types of bursting oscillations such as sub Hopf/sub Hopf burster, sub Hopf/fold-cycle burster, and doublefold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states（QSs） and the repetitive spiking states（SPs） may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically.
