Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take incli...Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.展开更多
A non-resonant piezoelectric linear motor with a flexible driving end,which has an extensive working frequency range and good operation stability,is studied theoretically and experimentally.Based on the microscopic vi...A non-resonant piezoelectric linear motor with a flexible driving end,which has an extensive working frequency range and good operation stability,is studied theoretically and experimentally.Based on the microscopic vibration characteristics of the motor stator,the longitudinal vibration model is established for the whole motor system.According to the Coulomb friction model and the motor vibration model,the friction mechanism of the nonresonant piezoelectric linear motor is investigated by dynamical analysis of the whole motor system.Furthermore,the vibration characteristics and mechanical output characteristics of the stator are simulated and experimentally studied on the basis of the friction drive mechanism model.Finally,both the simulation and experimental results show that this kind of motor remain stable in the frequency domain from 2.2 kHz to 3.5 kHz and that when the pre-stress is 4 Nand the driving voltage is 90 V,the maximum velocity of the motor is above 4 mm/s and the maximum thrust is nearly 0.5 N.展开更多
Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ ...Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ εQ（ t） ）x ＋ eg（t） ＋ h（x, t）, where A is a constant matrix with multiple eigenvalues; h = O（x2） （x-4）） ; and h（x, t）, Q（t）, and g（t） are analytic quasi-periodic with respect to t with the same frequencies. Under suitable hypotheses of non-resonance conditions and non-degeneracy conditions, for most sufficiently small ε, the system can be reducible to a nonlinear quasi-periodic system with an equilibrium point by means of a quasi-periodic transformation.展开更多
In this article, we study the solvability of nonlinear problem for p-Laplacian with nonlinear boundary conditions. We give some characterization of the first eigenvalue of an intermediary eigenvalne problem as simplic...In this article, we study the solvability of nonlinear problem for p-Laplacian with nonlinear boundary conditions. We give some characterization of the first eigenvalue of an intermediary eigenvalne problem as simplicity, isolation and its strict monotonicity. Afterward, we character also the second eigenvalue and its strictly partial monotony. On the other hand, in some sense, we establish the non-resonance below the first and furthermore between the first and second eigenvalues of nonlinear Steklov-Robin.展开更多
Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-princi...Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and l-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained.展开更多
基金This paper was completed when the first author was visiting East China Normal University.This work was supported by the National Natural Science Foundation of China(Grant No.10071022).
文摘Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.
基金supported by the National Natural Science Foundations of China(Nos.51405420,51375224,61503319)the Natural Science Foundation of Jiangsu Province(No.BK20140474)+2 种基金the Sponsorship of Jiangsu Oversea Research and Training Program for University Prominent Young&Middle-aged Teachersthe Jiangsu Province Ordinary University Professional Degree Graduate Innovation Project(No.SJZZ16_0294)Qing Lan Project of Jiangsu Higher Education of China(No.Su-Teacher2018-12)
文摘A non-resonant piezoelectric linear motor with a flexible driving end,which has an extensive working frequency range and good operation stability,is studied theoretically and experimentally.Based on the microscopic vibration characteristics of the motor stator,the longitudinal vibration model is established for the whole motor system.According to the Coulomb friction model and the motor vibration model,the friction mechanism of the nonresonant piezoelectric linear motor is investigated by dynamical analysis of the whole motor system.Furthermore,the vibration characteristics and mechanical output characteristics of the stator are simulated and experimentally studied on the basis of the friction drive mechanism model.Finally,both the simulation and experimental results show that this kind of motor remain stable in the frequency domain from 2.2 kHz to 3.5 kHz and that when the pre-stress is 4 Nand the driving voltage is 90 V,the maximum velocity of the motor is above 4 mm/s and the maximum thrust is nearly 0.5 N.
文摘Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ εQ（ t） ）x ＋ eg（t） ＋ h（x, t）, where A is a constant matrix with multiple eigenvalues; h = O（x2） （x-4）） ; and h（x, t）, Q（t）, and g（t） are analytic quasi-periodic with respect to t with the same frequencies. Under suitable hypotheses of non-resonance conditions and non-degeneracy conditions, for most sufficiently small ε, the system can be reducible to a nonlinear quasi-periodic system with an equilibrium point by means of a quasi-periodic transformation.
文摘In this article, we study the solvability of nonlinear problem for p-Laplacian with nonlinear boundary conditions. We give some characterization of the first eigenvalue of an intermediary eigenvalne problem as simplicity, isolation and its strict monotonicity. Afterward, we character also the second eigenvalue and its strictly partial monotony. On the other hand, in some sense, we establish the non-resonance below the first and furthermore between the first and second eigenvalues of nonlinear Steklov-Robin.
基金Project supported by the National Natural Science Foundation of China (No. 10471087) the Zhejiang Provincial Natural Science Foundation of China (No.Y605044).
文摘Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and l-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained.
