In this paper we investigate spatiotemporal pattern formation in excitable media with only a long-range link. Besides the trivial solutions of spiral patterns, we find the asymptotic self-sustained target waves in the...In this paper we investigate spatiotemporal pattern formation in excitable media with only a long-range link. Besides the trivial solutions of spiral patterns, we find the asymptotic self-sustained target waves in the autonomous tissues. The wave source supporting this kind of new pattern is the oscillatory one-dimensional Winfree-loop self- organized under the presence of a long-range link, which is explored by the dominant phase-advanced driving method. Based on this understanding we can effectively regulate the oscillations of excitable media by suitably arranging the long-range link, including construction of self-sustained target waves with controllable period and wave length, or manipulation of system states between different patterns.展开更多
This paper investigates antispiral wave breakup phenomena in coupled two-dimensional FitzHugh-Nagumo cells with self-sustained oscillation via Hopf bifurcation. When the coupling strength of the active variable decrea...This paper investigates antispiral wave breakup phenomena in coupled two-dimensional FitzHugh-Nagumo cells with self-sustained oscillation via Hopf bifurcation. When the coupling strength of the active variable decreases to a critical value, wave breakup phenomenon first occurs in the antispiral core region where waves collide with each other and spontaneously break into spatiotemporal turbulence. Measurements reveal for the first time that this breakup phenomenon is due to the mechanism of antispiral Doppler instability.展开更多
The influence of long-range links on spiral waves in an excitable medium has been investigated. Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connecti...The influence of long-range links on spiral waves in an excitable medium has been investigated. Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connection probability P. Spiral waves with few perturbations, broken spiral waves, pseudo spiral turbulence, synchronous oscillations, and homogeneous rest state are discovered under different network structures. Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns. The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state. Finally, we use long-range links to successfully control spiral waves and spiral turbulence.展开更多
基金the National Natural Science Foundation of China(10662002),the Natural Science Foundation of Guangxi Zhuang Autonomous Region(Grant No.640003)and the Innovation Project of Guangxi Graduate Education(Grant No.2006105930702M15)
基金supported by the National Natural Science Foundation of China (Grant No. 11047146)the Science Foundation of the Education Bureau of Shaanxi Province of China (Grant No. 11JK0544)+1 种基金the Natural Science Foundation of Shaanxi Province of China (Grant No. 2010JQ1014)the Science Foundation of Baoji University of Arts and Sciences (Grant Nos. ZK1048 andZK1049)
文摘In this paper we investigate spatiotemporal pattern formation in excitable media with only a long-range link. Besides the trivial solutions of spiral patterns, we find the asymptotic self-sustained target waves in the autonomous tissues. The wave source supporting this kind of new pattern is the oscillatory one-dimensional Winfree-loop self- organized under the presence of a long-range link, which is explored by the dominant phase-advanced driving method. Based on this understanding we can effectively regulate the oscillations of excitable media by suitably arranging the long-range link, including construction of self-sustained target waves with controllable period and wave length, or manipulation of system states between different patterns.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10675020)by the National Basic Research Program of China (973 Program) (Grant No. 2007CB814800)
文摘This paper investigates antispiral wave breakup phenomena in coupled two-dimensional FitzHugh-Nagumo cells with self-sustained oscillation via Hopf bifurcation. When the coupling strength of the active variable decreases to a critical value, wave breakup phenomenon first occurs in the antispiral core region where waves collide with each other and spontaneously break into spatiotemporal turbulence. Measurements reveal for the first time that this breakup phenomenon is due to the mechanism of antispiral Doppler instability.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11105003)the Science Foundation of the Education Bureau of Shaanxi Province of China (Grant No. 11JK0544)
文摘The influence of long-range links on spiral waves in an excitable medium has been investigated. Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connection probability P. Spiral waves with few perturbations, broken spiral waves, pseudo spiral turbulence, synchronous oscillations, and homogeneous rest state are discovered under different network structures. Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns. The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state. Finally, we use long-range links to successfully control spiral waves and spiral turbulence.
