Propagation failure in excitable media
نویسندگان
چکیده
We study a mechanism of pulse propagation failure in excitable media where stable traveling pulse solutions appear via a subcritical pitchfork bifurcation. The bifurcation plays a key role in that mechanism. Small perturbations, externally applied or from internal instabilities, may cause pulse propagation failure ~wave breakup! provided the system is close enough to the bifurcation point. We derive relations showing how the pitchfork bifurcation is unfolded by weak curvature or advective field perturbations and use them to demonstrate wave breakup. We suggest that the recent observations of wave breakup in the Belousov-Zhabotinsky reaction induced by either an electric field @J.J. Taboada et al.. Chaos 4, 519 ~1994!# or a transverse instability @M. Markus, G. Kloss, and I. Kusch, Nature ~London! 371, 402 ~1994!# are manifestations of this mechanism. @S1063-651X~97!11512-4#
منابع مشابه
A ug 2 00 4 On propagation failure in 1 and 2 dimensional excitable media
We present a non-perturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and twodimensional excitable media. In one-dimensional media we describe the behaviour of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point wher...
متن کاملOn propagation failure in one- and two-dimensional excitable media.
We present a nonperturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behavior of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point where...
متن کاملWave trains, self-oscillations and synchronization in discrete media
We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed, as well as the critical coupling and the critical separation of time scales for propagation failure. It describes stable wave train generation by repeated fir...
متن کاملHomogenization and Flame Propagation in Periodic Excitable Media: the Asymptotic Speed of Propagation
We study the effect of homogenization on flame propagation in periodic excitable media, when the width of the flame is much smaller than the characteristic size of the heterogeneities.
متن کاملWave Propagation in Excitable Media with Randomly Distributed Obstacles
We study the effect of small, randomly distributed obstacles on wave propagation in two-dimensional (2D) and 3D excitable media described by the Aliev–Panfilov model. We find that increasing the number of obstacles decreases the conduction velocity of plane waves and decreases the effective diffusion coefficient in the eikonal curvature equation. The presence of obstacles also increases the ind...
متن کامل