Andrei Bukh

We study the spike activity of two mutually coupled FitzHugh – Nagumo neurons, which is influenced by two-frequency signals. The ratio of frequencies in the external signal corresponds to musical intervals (consonances). It has been discovered that this system can exhibit selective properties for identifying musical intervals. The mechanism of selectivity is shown, which is associated with the influence on the spiking frequency of neurons by intensity of the external signal and nature of the interaction of neurons.

The present work is devoted to the detailed quantification of the transition from spiral waves to spiral wave chimeras in a network of self-sustained oscillators with twodimensional geometry. The basic elements of the network under consideration are the van der Pol oscillator or the FitzHugh – Nagumo neuron. Both of the models are in the regime of relaxation oscillations. We analyze the regime by using the indices of local sensitivity, which enables us to evaluate the sensitivity of each oscillator at a finite time. Spiral waves are observed in both lattices when the interaction between elements has a local character. The dynamics of all the elements is regular. There are no pronounced high-sensitive regions. We have discovered that, when the coupling becomes nonlocal, the features of the system change significantly. The oscillation regime of the spiral wave center element switches to a chaotic one. Besides, a region with high sensitivity occurs around the wave center oscillator. Moreover, we show that the latter expands in space with elongation of the coupling range. As a result, an incoherence cluster of the spiral wave chimera is formed exactly within this high-sensitive area. A sharp increase in the values of the maximal Lyapunov exponent in the positive region leads to the formation of the incoherence cluster. Furthermore, we find that the system can even switch to a hyperchaotic regime when several Lyapunov exponents become positive.

The influence of noise on chimera states arising in ensembles of nonlocally coupled chaotic maps is studied. There are two types of chimera structures that can be obtained in such ensembles: phase and amplitude chimera states. In this work, a series of numerical experiments is carried out to uncover the impact of noise on both types of chimeras. The noise influence on a chimera state in the regime of periodic dynamics results in the transition to chaotic dynamics. At the same time, the transformation of incoherence clusters of the phase chimera to incoherence clusters of the amplitude chimera occurs. Moreover, it is established that the noise impact may result in the appearance of a cluster with incoherent behavior in the middle of a coherence cluster.