What explanation can we give for the generation of spiral waves in a excitable medium? I was thinking about the reason for the generation of spiral waves (a.k.a scroll waves) like in BZ reactions and Fitzhugh-Nagumo systems. 
Can someone give me some explanation or references ?
 A: I assume that you already understand how planar waves propagate in an excitable medium from this question of yours.
An easy understanding of spiral waves in an excitable medium can be obtained by looking at a spacially, temporally and state-wise discretised model of an excitable medium:


*

*The space is a regular lattice (chess board), with each field / patch / unit / point representing an excitable unit. I do not pay much attention to the size and borders of this lattice as they don’t matter.

*Each unit has three states:


*

*white: inactive

*red: excited

*blue: inhibitory


*With each time step, the state of each field changes as follows:


*

*2→3: If the field was excited, it now is inhibitory.

*3→1: If the field was inhibitory, it is now inactive.

*If the unit was inactive and an adjacent unit was excited, it is now excited itself.
It is hopefully easy to see, that this model has all elemental properties of excitable media, such as allowing for the propagation of circular waves, planar waves and wavefronts that extinguish each other.
For example, a propagating planar wavefront would look like this and move one field upwards each step:

Now, suppose our model is in this state:

It is hopefully easy to see that the state for the next time step is the following (ignore the borders, the important things happen in the centre):

Now, this is the same state as before, just rotated clockwise by π/2. Consequently, after three further time steps, our system returns to its initial state. Thus, we have found a periodic state with a period of four, which is a spiral wave.
If you start our model system with a single patch of excitation (and inactivity elsewhere), you will obtain a circular wave, but many other initial conditions will eventually produce such spiral waves. Moreover, if you start with a single patch of excitation and have some inhomogeneities (i.e., fields that behave differently or missing connections between fields), the latter can “break” the wave and make it a spiral wave (which usually pins around an inhomogeneity).
In a continuous excitable medium, things are more complex, but the general mechanisms are the same.
A: An excitable medium can create spirals. The BZ reaction and the Fitzhugh-Nagumo equations have regions of parameters where excitability occurs. If you excite above the excitability threshold such a medium in a point, you create there a pulsed response. After the pulse, the medium has to recover before a second pulse can be excited ("refractory time"). This local perturbation (a pulse in space and time) excites the neighboring regions triggering the same behavior. In this way, the local perturbation spreads out as a propagating front. With perfect symmetry, this leads to an expanding ring. I think spirals occur from there when some asymmetry or defect is present, or two fronts collide.
You can find more details in scholarpedia:

In two-dimensional excitable media, one can observe expanding target patterns and rotating spiral waves. In three dimensions, rotating scroll waves are possible. All these dynamic phenomena represent well-known examples of self-organization in complex systems resulting in pattern formation.
The structure and the properties of the self-organized patterns are established due to a balance between the energy influx from internal distributed sources and the energy dissipation. Thus, the spatio-temporal patterns in excitable media belong to self-organization processes, which occur far away from the thermodynamical equilibrium.

Here you can play with a Java applet simulating a 2D excitable medium.
An important real system modeled in this way is the heart: cardiac myocites are excitable cells (like neurons), and their excitable electric response is coupled to mechanical contraction. At each beat, an excitable front propagates from the top of the heart (sinus node) to the bottom, contracting in the right way the heart volume. Spirals in the front are supposed to be linked with deadly arrhythmia (video).
A: Here is a video of a (simulated) fire front spreading through a forest, that illustrates the genesis of spiral waves:
https://www.youtube.com/watch?v=HqokhwFO5hY


The initial planar flame front is broken, because of a raincloud that hovers over the upper half of the forest. Luckily for our purposes it dissappears just in time after the flame front passes it. Then the half front starts to curl in around its open tip.
The trick is to set the regrowth rate of the trees high enough, so that there is always enough wood to burn. I think this point illustrates very nicely, that spiral waves need a dissipative medium to exist.
Regarding the literature question: The book "Synergetics I" by Alexander Mikhailov is a great source of information on spiral dynamics. He worked on the kinematical description of spiral and scroll wave dynamics. The example sketch in the accepted answer can be found in his book in more detail.
Regarding spiral wave genesis: As you can see in the video, usually excitable systems start with a planar wave that gets "broken" by some kind of obstacle, e.g. some elements are not excitable anymore. In the heart this could be scar tissue or blood vessels or even just old cells that do not pass on the electrical excitation fast enough anymore. However, it is also possible to create spirals without obstacles, for example the normal heart contraction can convert a planar wave to a spiral wave.
