If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unco...If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.展开更多
In this paper a modified L-P method and multiple scale method are used to solve sub-harmonic resonance solutions of strong and nonlinear resonance of general Van der Pol equation with parametric and external excitatio...In this paper a modified L-P method and multiple scale method are used to solve sub-harmonic resonance solutions of strong and nonlinear resonance of general Van der Pol equation with parametric and external excitations by parametric transformation. Bifurcation response equation and transition sets of sub-harmonic resonance with strong nonlinearity of general Van der Pol equation with parametric and external excitation are worked out.Besides, transition sets and bifurcation graphs are drawn to help to analysis the problems theoretically. Conclusions show that the transition sets of general and nonlinear Van der Pol equation with parametric and external excitations are more complex than those of general and nonlinear Van der Pol equation only with parametric excitation, which is helpful for the qualitative and quantitative reference for engineering and science applications.展开更多
Let M be a closed smooth manifold M, and let f ： M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set A of f. We show that if f has the C^1-stably average shadowing property on A, then A...Let M be a closed smooth manifold M, and let f ： M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set A of f. We show that if f has the C^1-stably average shadowing property on A, then A admits a dominated splitting.展开更多
In this paper,a novel multi-frame track-before-detect algorithm is proposed,which is based on root label clustering to reduce the high computational complexity arising by observation area expansion and clutter/noise d...In this paper,a novel multi-frame track-before-detect algorithm is proposed,which is based on root label clustering to reduce the high computational complexity arising by observation area expansion and clutter/noise density increase.A criterion of track extrapolation is used to construct state transition set,root label is marked by state transition set to obtain the distribution information of multiple targets in measurement space,then measurement plots of multi-frame are divided into several clusters,and finally multi-frame track-before-detect algorithm is implemented in each cluster.The computational complexity can be reduced by employing the proposed algorithm.Simulation results show that the proposed algorithm can accurately detect multiple targets in close proximity and reduce the number of false tracks.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10872142 and10632040)the New Century Excellent Talents Plan of the Ministry of Education of China(No. NCET-05-0247)the Key Project of Tianjin (No. 09JCZDJC26800)
文摘If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.
基金Supported by the National Natural Science Foundation of China（11201118）
文摘In this paper a modified L-P method and multiple scale method are used to solve sub-harmonic resonance solutions of strong and nonlinear resonance of general Van der Pol equation with parametric and external excitations by parametric transformation. Bifurcation response equation and transition sets of sub-harmonic resonance with strong nonlinearity of general Van der Pol equation with parametric and external excitation are worked out.Besides, transition sets and bifurcation graphs are drawn to help to analysis the problems theoretically. Conclusions show that the transition sets of general and nonlinear Van der Pol equation with parametric and external excitations are more complex than those of general and nonlinear Van der Pol equation only with parametric excitation, which is helpful for the qualitative and quantitative reference for engineering and science applications.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(Grant No.2011-0007649)supported by National Natural Science Foundation of China(Grant No.11026041)
文摘Let M be a closed smooth manifold M, and let f ： M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set A of f. We show that if f has the C^1-stably average shadowing property on A, then A admits a dominated splitting.
基金supported by the Innovation Project of Science and Technology Commission of the Central Military Commission,China(No.19-HXXX-01-ZD-006-XXX-XX)。
文摘In this paper,a novel multi-frame track-before-detect algorithm is proposed,which is based on root label clustering to reduce the high computational complexity arising by observation area expansion and clutter/noise density increase.A criterion of track extrapolation is used to construct state transition set,root label is marked by state transition set to obtain the distribution information of multiple targets in measurement space,then measurement plots of multi-frame are divided into several clusters,and finally multi-frame track-before-detect algorithm is implemented in each cluster.The computational complexity can be reduced by employing the proposed algorithm.Simulation results show that the proposed algorithm can accurately detect multiple targets in close proximity and reduce the number of false tracks.
