A system of three-unit networks with no self-connection is investigated, the general formula for bifurcation direction of Hopf bifurcation is calculated, and the estimaion formula of the period for periodic solution i...A system of three-unit networks with no self-connection is investigated, the general formula for bifurcation direction of Hopf bifurcation is calculated, and the estimaion formula of the period for periodic solution is given.展开更多
In this paper we give an applicable parameter formula about the bifurcationand stability of periodic solution for a four-dimensional differential system. By using thisresult in a simple electronic neural network syste...In this paper we give an applicable parameter formula about the bifurcationand stability of periodic solution for a four-dimensional differential system. By using thisresult in a simple electronic neural network system, we obtain a strict condition of theexistence of periodic solution.展开更多
The wash-out filter （WF） technique is used to control the flutter of a two dimensional airfoil with cubic non-linearity in incompressible flow. Firstly, Hopf bifurcation theory is used to determine the point at whic...The wash-out filter （WF） technique is used to control the flutter of a two dimensional airfoil with cubic non-linearity in incompressible flow. Firstly, Hopf bifurcation theory is used to determine the point at which the nonlinear controller is introduced. The system is then transformed into Jordan canonical form, based on analysis of linearized eigenvalues of the system. Secondly, for the introduced WF controller, the linear control gain is determined according to Hopf bifurcation condition. The sym- bolic computing program of normal form direct method （NFDM） is also used to obtain the normal form of the controlled system. The non-linear control gain can be determined based on the relation of the type of bifurcation and the parameters of the normal form, to transform sub-critical Hopf bifurcation to be su- per-critical one. Lastly, numerical simulations are used to certify the validity of theoretical analysis, in which the amplitude of flutter or limit cycle of the controlled system is reduced greatly, comparing to the original system.展开更多
A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular pl...A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.展开更多
基金the National Natural Science Foundation of China (No.19972058) and theApplied Science Foundation of Yunnan, China.
文摘A system of three-unit networks with no self-connection is investigated, the general formula for bifurcation direction of Hopf bifurcation is calculated, and the estimaion formula of the period for periodic solution is given.
文摘In this paper we give an applicable parameter formula about the bifurcationand stability of periodic solution for a four-dimensional differential system. By using thisresult in a simple electronic neural network system, we obtain a strict condition of theexistence of periodic solution.
文摘The wash-out filter （WF） technique is used to control the flutter of a two dimensional airfoil with cubic non-linearity in incompressible flow. Firstly, Hopf bifurcation theory is used to determine the point at which the nonlinear controller is introduced. The system is then transformed into Jordan canonical form, based on analysis of linearized eigenvalues of the system. Secondly, for the introduced WF controller, the linear control gain is determined according to Hopf bifurcation condition. The sym- bolic computing program of normal form direct method （NFDM） is also used to obtain the normal form of the controlled system. The non-linear control gain can be determined based on the relation of the type of bifurcation and the parameters of the normal form, to transform sub-critical Hopf bifurcation to be su- per-critical one. Lastly, numerical simulations are used to certify the validity of theoretical analysis, in which the amplitude of flutter or limit cycle of the controlled system is reduced greatly, comparing to the original system.
基金The Project supported by the NationalGansu Province Natural Science Foundation of China
文摘A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.
