Active medium

The results of investigation of reaction-diffusion type models demonstrating diffusion instability are presented. In particular, in general case the condition for both Turing and wave instabilities are obtained for  three equations of this type with the diagonal diffusion matrix. Qualitative properties of the system, in which bifurcations of each of the two types can take place, are clarified. Investigation of a set of amplitude equations, describing interaction of several modes which became unstable due to the wave bifurcation, is carried out.

This paper presents two new methods of suppressing an impulse in one-dimensional and two-dimensional excitable media using an external influence. In the proposed methods, we used short-impulseinfluence, leading to a change in velocity of the front , which in turn led to the destabilization of  the propagating impulse and transition medium unexcited state. The studies were conducted on the Zykov model that a certain set of parameters is a model of an excitable medium.

Investigation of a set of amplitude equations, describing interaction of several modes which became unstable due to the wave bifurcation, is carried out. It is shown that as a result of competition between modes depending on the value of the parameter defining the strength of interaction only two regimes are possible: either quasi one-dimensional travelling waves (there exists only one nonzero mode) or standing waves (al the modes are nonzero).