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
Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the syste...Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.展开更多
It is demonstrated that defects of any shape or size can be doped in holographic photonic crystals using a cw visible laser and spherical/cylindrical lens. Defects with different sizes at any depth in the material can...It is demonstrated that defects of any shape or size can be doped in holographic photonic crystals using a cw visible laser and spherical/cylindrical lens. Defects with different sizes at any depth in the material can be obtained by controlling the position of the foca/point of the lens and exposure value. We facilitate the implementation of sub-wavelength arbitrary point or line defects in large-size 2D holographic photonic crystals.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Project supported by the National Nature Science Foundation of China(Grant No.11205044)the Fundamental Research Funds for the Central Universities(Grant No.10ML40)
文摘Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.
基金Supported by the National Natural Science Foundation of China under Grant Nos 60277014 and 60677006, and the Research Program for Under-Graduate Student of the Ministry of Education of China.
文摘It is demonstrated that defects of any shape or size can be doped in holographic photonic crystals using a cw visible laser and spherical/cylindrical lens. Defects with different sizes at any depth in the material can be obtained by controlling the position of the foca/point of the lens and exposure value. We facilitate the implementation of sub-wavelength arbitrary point or line defects in large-size 2D holographic photonic crystals.
