ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


диффузионная неустойчивость

Spatial-temporal patterns in a multidimensional active medium formed due to polymodal interaction near the wave bifurcation

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).

Spatial-temporal patterns in active medium caused by diffusion instability

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.

Oscillatory instability and spontaneous subthreshold oscillations in a network of diffusively coupled calcium oscillators

The paper is devoted to the investigation of the dynamics of a network of interacting astrocytes. The astrocytes represent brain glial cells capable to generate chemical activity signals (calcium pulses). Similarly to nerve cells (neurons) the astrocytes form networks of interacting units coupled by means of gap junctions. The junctions represent special protein channels providing the diffusion of chemically active species between neighboring cells.