In this paper, we study the number of limit cycles appeared in Hopf bifurcations of a Lienard system with multiple parameters. As an application to some polynomial Lienard systems of the form x= y, y= -gin（x） - fn...In this paper, we study the number of limit cycles appeared in Hopf bifurcations of a Lienard system with multiple parameters. As an application to some polynomial Lienard systems of the form x= y, y= -gin（x） - fn（X）y, we obtain a new lower bound of maximal number of limit cycles which appear in Hopf bifurcation for arbitrary degrees m and n.展开更多
This paper deals with a kind of fourth degree systems with perturbations. By using the method of multi-parameter perturbation theory and qualitative analysis, it is proved that the system can have six limit cycles.
For the quadratic system: x=-y+δx + lx2 + ny2, y=x(1+ax-y) under conditions -1<l<0,n+l - 1>0 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notic...For the quadratic system: x=-y+δx + lx2 + ny2, y=x(1+ax-y) under conditions -1<l<0,n+l - 1>0 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notice that when na2+l < 0 the system has one saddleN(0,1/n) and three anti-saddles.展开更多
This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system.Based on three-dimensional Hopf bifurcation theorem,the ...This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system.Based on three-dimensional Hopf bifurcation theorem,the existence of limit cycles is first proved.Then the homotopy analysis method(HAM) is applied to obtain the analytical approximations of the limit cycle and its frequency.In deriving the higher-order approximations,the authors utilized the idea of a perturbation procedure proposed for limit cycles' approximation in van der Pol equation.By comparing with the numerical integration solutions,it is shown that the accuracy of the analytical results obtained in this paper is very high,even when the amplitude of the limit cycle is large.展开更多
A numerical study of a standing-wave thermoacoustic engine is presented. The aim of this work is to study the effect of increasing the heat exchangers length on the acoustic power. The analysis of the flow and the pre...A numerical study of a standing-wave thermoacoustic engine is presented. The aim of this work is to study the effect of increasing the heat exchangers length on the acoustic power. The analysis of the flow and the prediction of the heat transfer are performed by solving the non linear unsteady Navier-Stocks equations using the finite volume method implemented in -ANSYS CFX- CFD code. The results show an increase in the limit cycle acoustic pressure and power as well as the specific work per cycle with the increase of heat exchangers length.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11271261)
文摘In this paper, we study the number of limit cycles appeared in Hopf bifurcations of a Lienard system with multiple parameters. As an application to some polynomial Lienard systems of the form x= y, y= -gin（x） - fn（X）y, we obtain a new lower bound of maximal number of limit cycles which appear in Hopf bifurcation for arbitrary degrees m and n.
基金Project supported by the National Natural Science Foundation of China (No.10371072)the New Century Excellent Ttdents in University (No.NCBT-04-038)the Shanghai Leading Academic Discipline (No.T0401).
文摘This paper deals with a kind of fourth degree systems with perturbations. By using the method of multi-parameter perturbation theory and qualitative analysis, it is proved that the system can have six limit cycles.
基金Project supported by the National Natural Science Foundation of China
文摘For the quadratic system: x=-y+δx + lx2 + ny2, y=x(1+ax-y) under conditions -1<l<0,n+l - 1>0 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notice that when na2+l < 0 the system has one saddleN(0,1/n) and three anti-saddles.
基金supported by the National Natural Science Foundations of China under Grant Nos.11201072 and 11102041the China Postdoctoral Science Foundation under Grant No.2011M500803Education Department of Fujian Province under Grant No.JA10065
文摘This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system.Based on three-dimensional Hopf bifurcation theorem,the existence of limit cycles is first proved.Then the homotopy analysis method(HAM) is applied to obtain the analytical approximations of the limit cycle and its frequency.In deriving the higher-order approximations,the authors utilized the idea of a perturbation procedure proposed for limit cycles' approximation in van der Pol equation.By comparing with the numerical integration solutions,it is shown that the accuracy of the analytical results obtained in this paper is very high,even when the amplitude of the limit cycle is large.
文摘A numerical study of a standing-wave thermoacoustic engine is presented. The aim of this work is to study the effect of increasing the heat exchangers length on the acoustic power. The analysis of the flow and the prediction of the heat transfer are performed by solving the non linear unsteady Navier-Stocks equations using the finite volume method implemented in -ANSYS CFX- CFD code. The results show an increase in the limit cycle acoustic pressure and power as well as the specific work per cycle with the increase of heat exchangers length.
