Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopfbifurcations is studied in a reaction-diffusion equation.The time delay changes remarkably the oscillation frequen...Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopfbifurcations is studied in a reaction-diffusion equation.The time delay changes remarkably the oscillation frequency,theintrinsic wave vector,and the intensities of both Turing and Hopf modes.The application of appropriate time delaycan control the competition between the Turing and Hopf modes.Analysis shows that individual or both feedbacks canrealize the control of the transformation between the Turing and Hopf patterns.Two-dimensional numerical simulationsvalidate the analytical results.展开更多
By End（G） and hEnd（G） we denote the set of endomorphisms and half-strong endomorphisms of a graph G respectively. A graph G is said to be E-H-unretractive if End（G） = hEnd（G）. A general characterization of an ...By End（G） and hEnd（G） we denote the set of endomorphisms and half-strong endomorphisms of a graph G respectively. A graph G is said to be E-H-unretractive if End（G） = hEnd（G）. A general characterization of an E-H-unretractive graph seems to be difficult. In this paper, bipartite graphs with E-H-unretractivity are characterized explicitly.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No. 09ML56the Foundation for Young Teachers of the North China Electric Power University, China under Grant No. 200611029
文摘Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopfbifurcations is studied in a reaction-diffusion equation.The time delay changes remarkably the oscillation frequency,theintrinsic wave vector,and the intensities of both Turing and Hopf modes.The application of appropriate time delaycan control the competition between the Turing and Hopf modes.Analysis shows that individual or both feedbacks canrealize the control of the transformation between the Turing and Hopf patterns.Two-dimensional numerical simulationsvalidate the analytical results.
基金the National Natural Science Foundation of China （No. 10671122）.Acknowledgement The author would like to thank Professor Dr. U.Knauer for valuable advice and helpful comments on this paper.
文摘By End（G） and hEnd（G） we denote the set of endomorphisms and half-strong endomorphisms of a graph G respectively. A graph G is said to be E-H-unretractive if End（G） = hEnd（G）. A general characterization of an E-H-unretractive graph seems to be difficult. In this paper, bipartite graphs with E-H-unretractivity are characterized explicitly.
