Using the Greenberg-Hasting cellular automata model, we study the properties of target waves in excitable media under the no-flux boundary conditions. For the system has only one excited state, the computer simulation...Using the Greenberg-Hasting cellular automata model, we study the properties of target waves in excitable media under the no-flux boundary conditions. For the system has only one excited state, the computer simulation and analysis lead to the conclusions that, the number of refractory states does not influence the wave-front speed; the wave- front speed decreases as the excitation threshold increases and increases as the neighbor radius increases; the period of target waves is equal to the number of cell states; the excitation condition for target waves is that the wave-front speed must be bigger than half of the neighbor radius.展开更多
With help of establishing the moving coordinate on the wave front surface and the perturbation analysis in the boundary layer,the structures of wave front and organization center in excitable media were studied. The e...With help of establishing the moving coordinate on the wave front surface and the perturbation analysis in the boundary layer,the structures of wave front and organization center in excitable media were studied. The eikonal equation of wave front surface and general equation of organization center were obtained. These eikonal equations reveal the wave front surfaces have structures of twisted scroll wave and Mbius band, the organization centers have structures of knotted and linked ring. These theoretical results not only explain the wave patterns of BZ(Belousov-Zhabotinskii) chemical reaction but also give several possibility structures of wave front surface and organization center in general excitable media.展开更多
The motion of organization center of three_dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear...The motion of organization center of three_dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear law are derived for untwisted organization center. These results have explicit physical meaning and are in good agreement with experiments.展开更多
We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coup...We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coupling strength, the synchronization is broken down. With the further increase of the coupling strength, complete synchronization and phase synchronization occur again. We also found that the inhomogeneity in excitable systems is helpful to the synchronization.展开更多
Spirals generated from the excitable media within the Barkley model is investigated under the gradient electric fields by a numerical simulation. The spiral drift and spiral break up are observed when the amplitude of...Spirals generated from the excitable media within the Barkley model is investigated under the gradient electric fields by a numerical simulation. The spiral drift and spiral break up are observed when the amplitude of the electric fields is modulated by a constant signal or a chaotic signal. It is also verified that, even in the presence of the white noise, the whole system can reach homogeneous states after the spiral breakup, by using an adaptive strategy.展开更多
In this paper, an intermittent local electric shock scheme is proposed to suppress stable spiral waves in the Barkley model by a weak electric shock （about 0.4 to 0.7） imposed on a random selected n × n grids ...In this paper, an intermittent local electric shock scheme is proposed to suppress stable spiral waves in the Barkley model by a weak electric shock （about 0.4 to 0.7） imposed on a random selected n × n grids （n =1 - 5, compared with the original 256×256 lattice） and monitored synchronically the evolutions of the activator on the grids as the sampled signal of the activator steps out a given threshold （i.e., the electric shock works on the n ~ n grids if the activator u ≤ 0.4 or u ≥ 0.8）. The numerical simulations show that a breakup of spiral is observed in the media state evolution to finally obtain homogeneous states if the electric shock with appropriate intensity is imposed.展开更多
The transition from stationary to oscillatory states in dynamical systems under phase space compression is investigated. By considering the model for the spatially one-dimensional complex Ginzburg-Landau equation, we ...The transition from stationary to oscillatory states in dynamical systems under phase space compression is investigated. By considering the model for the spatially one-dimensional complex Ginzburg-Landau equation, we find that defect turbulence can be substituted with stationary and oscillatory signals by applying system perturbation and confining variable into various ranges. The transition procedure described by the oscillatory frequency is studied via numerical simulations in detail.展开更多
We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory. In particular fo...We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory. In particular for the excitable media with equal diffusion, we obtain a close system for the motion of the filament. With an example of the Oregonator model, our results are in good agreement with those simulated by Winfree.展开更多
We study dynamics of spiral waves under a uniform periodic temporal forcing in an excitable medium. With a specific combination of frequency and amplitude of the external periodic forcing, a resonance drift of a spira...We study dynamics of spiral waves under a uniform periodic temporal forcing in an excitable medium. With a specific combination of frequency and amplitude of the external periodic forcing, a resonance drift of a spiral wave occurs along a straight line, and it is accompanied by a complicated ‘flower-like＇ motion on each side of this bifurcate boundary line. It is confirmed that the straight-line drift frequency of spiral waves is not locked to the nature rotation frequency as the forcing amplitude expends are further verified numerically for a simplified kinematical the range of the spiral wave frequency. These results model.展开更多
By Painleve analysis, traveling wave speed and solution of reaction-diffusion equations for the concentration of one species in one spatial dimension are in detail investigated. When the exponent of the creation term ...By Painleve analysis, traveling wave speed and solution of reaction-diffusion equations for the concentration of one species in one spatial dimension are in detail investigated. When the exponent of the creation term is larger than the one of the annihilation term, two typical cases are studied, one with the exact traveling wave solutions, yielding the values of speeds, the other with the series expansion solution, also yielding the value of speed. Conversely, when the exponent of creation term is smaller than the one of the annihilation term, two typical cases are also studied, but only for one of them, there is a series development solution, yielding the value of speed, and for the other, traveling wave solution cannot exist. Besides, the formula of calculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10562001 and 10765002
文摘Using the Greenberg-Hasting cellular automata model, we study the properties of target waves in excitable media under the no-flux boundary conditions. For the system has only one excited state, the computer simulation and analysis lead to the conclusions that, the number of refractory states does not influence the wave-front speed; the wave- front speed decreases as the excitation threshold increases and increases as the neighbor radius increases; the period of target waves is equal to the number of cell states; the excitation condition for target waves is that the wave-front speed must be bigger than half of the neighbor radius.
文摘With help of establishing the moving coordinate on the wave front surface and the perturbation analysis in the boundary layer,the structures of wave front and organization center in excitable media were studied. The eikonal equation of wave front surface and general equation of organization center were obtained. These eikonal equations reveal the wave front surfaces have structures of twisted scroll wave and Mbius band, the organization centers have structures of knotted and linked ring. These theoretical results not only explain the wave patterns of BZ(Belousov-Zhabotinskii) chemical reaction but also give several possibility structures of wave front surface and organization center in general excitable media.
文摘The motion of organization center of three_dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear law are derived for untwisted organization center. These results have explicit physical meaning and are in good agreement with experiments.
基金Project supported by the National Natural Science Foundation of China (Grant No 10305005)the Fundamental Research Fund for Physics and Mathematics of Lanzhou University, China
文摘We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coupling strength, the synchronization is broken down. With the further increase of the coupling strength, complete synchronization and phase synchronization occur again. We also found that the inhomogeneity in excitable systems is helpful to the synchronization.
基金Supported partially by the National Natural Science Foundation of China under Grant No 90303010.
文摘Spirals generated from the excitable media within the Barkley model is investigated under the gradient electric fields by a numerical simulation. The spiral drift and spiral break up are observed when the amplitude of the electric fields is modulated by a constant signal or a chaotic signal. It is also verified that, even in the presence of the white noise, the whole system can reach homogeneous states after the spiral breakup, by using an adaptive strategy.
文摘In this paper, an intermittent local electric shock scheme is proposed to suppress stable spiral waves in the Barkley model by a weak electric shock （about 0.4 to 0.7） imposed on a random selected n × n grids （n =1 - 5, compared with the original 256×256 lattice） and monitored synchronically the evolutions of the activator on the grids as the sampled signal of the activator steps out a given threshold （i.e., the electric shock works on the n ~ n grids if the activator u ≤ 0.4 or u ≥ 0.8）. The numerical simulations show that a breakup of spiral is observed in the media state evolution to finally obtain homogeneous states if the electric shock with appropriate intensity is imposed.
基金Supported in part by the National Natural Science Foundation of China under Grant Nos 10405018 and 70571053.
文摘The transition from stationary to oscillatory states in dynamical systems under phase space compression is investigated. By considering the model for the spatially one-dimensional complex Ginzburg-Landau equation, we find that defect turbulence can be substituted with stationary and oscillatory signals by applying system perturbation and confining variable into various ranges. The transition procedure described by the oscillatory frequency is studied via numerical simulations in detail.
文摘We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory. In particular for the excitable media with equal diffusion, we obtain a close system for the motion of the filament. With an example of the Oregonator model, our results are in good agreement with those simulated by Winfree.
基金Supported by the National Natural Science Foundation of China under Grant Nos 90303010 and 10405020.
文摘We study dynamics of spiral waves under a uniform periodic temporal forcing in an excitable medium. With a specific combination of frequency and amplitude of the external periodic forcing, a resonance drift of a spiral wave occurs along a straight line, and it is accompanied by a complicated ‘flower-like＇ motion on each side of this bifurcate boundary line. It is confirmed that the straight-line drift frequency of spiral waves is not locked to the nature rotation frequency as the forcing amplitude expends are further verified numerically for a simplified kinematical the range of the spiral wave frequency. These results model.
文摘By Painleve analysis, traveling wave speed and solution of reaction-diffusion equations for the concentration of one species in one spatial dimension are in detail investigated. When the exponent of the creation term is larger than the one of the annihilation term, two typical cases are studied, one with the exact traveling wave solutions, yielding the values of speeds, the other with the series expansion solution, also yielding the value of speed. Conversely, when the exponent of creation term is smaller than the one of the annihilation term, two typical cases are also studied, but only for one of them, there is a series development solution, yielding the value of speed, and for the other, traveling wave solution cannot exist. Besides, the formula of calculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media.
