The occurrence of Winfree turbulence is currently regarded as one of the principal mechanisms underlying cardiac fibrillation. We develop a local stimulation method that suppresses Winfree turbulence in three-dimensional excitable media. We find that Winfree turbulence can be effectively suppressed by locally injecting periodic signals to only a very small subset (around some surface region) of total space sites. Our method for the first time demonstrates the effectiveness of local low-amplitude periodic excitations in suppressing turbulence in 3D excitable media and has fundamental improvements in efficiency, convenience, and turbulence suppression speed compared with previous strategies. Therefore, it has great potential for developing into a practical low-amplitude defibrillation approach.

A method for suppressing spiral waves and spatiotemporal chaos in excitable media is proposed. Applying suitable periodic force to a single point, we can successfully suppress spiral waves as well as spatiotemporal chaos by generating target waves. After we turn off the external force, target waves finally disappear and the whole system which was in the state of spiral wave or spatiotemporal chaos goes to the spatially homogeneous steady state. It is shown that our control method is not sensitively model dependent. It works for a model for catalytic CO oxidation on platinum as well as for a model for cardiac muscle.

An effective method for controlling spiral turbulence in spatially extended systems is realized by introducing a spatially localized inhomogeneity into a two-dimensional system described by the complex Ginzburg-Landau equation. Our numerical simulations show that with the introduction of the inhomogeneity, a target wave can be produced, which will sweep all spiral defects out of the boundary of the system. The effects exist in certain parameter regions where the spiral waves are absolutely unstable. A theoretical explanation is given to reveal the underlying mechanism.

The drift behavior of spiral waves under the influence of a polarized electric field is investigated in the light that both the polarized electric field and the spiral waves possess rotation symmetry. Numerical simulations of a reaction-diffusion model show that the drift velocity of the spiral tip can be controlled by changing the polarization mode of the polarized electric field and some interesting drift phenomena are observed. When the electric field is circularly polarized and its rotation follows that of the spiral, the drift speed of the spiral tip reaches its maximal value. On the contrary, opposite rotation between the spiral and electric field locks the drift of the spiral tip. Analytical results based on the weak deformation approximation are consistent with the numerical results. We hope that our theoretical results will be observed in experiments, such as the Belousov-Zhabotinsky reaction.

A topological current is shown to exist in superconductivity. Using the $\phi$-mapping topological current theory, we have obtained a rigorous London equation with topological current, which reveals the inner relation between the condensate wave function $\psi$ and the induction $\overrightarrow{B}$. It is also shown that the equation is characterized by the Hopf index and Brouwer degree of $\phi$ mapping. As a result, the so-called modified London equation, which describes the distribution of the magnetic field for isolated vortices, is only a special case of the equation. Our theory, obtained without using any particular models or hypotheses, can also be applied to the illustration of a vortex-antivortex pair, vortex ring, and multicharged vortex.

Pinning of spiral waves by defects in cardiac muscle may cause permanent tachycardia. We numerically study the removal of a pinned spiral by a localized stimulus at the boundary of a two-dimensional excitable medium. It is shown that target waves may be generated by an external local force, and then the target waves will interact with the pinned spiral. When the external force is appropriately chosen, the generated target waves may suppress the pinned spiral, and the system is finally dominated by the target waves.