Tatyana Vadivasova

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.

We study numerically the spatio-temporal dynamics of a ring network of nonlocally coupled logistic maps when the coupling strength is modulated by colored Gaussian noise. Two cases of noise modulation are considered: 1) when the coupling coefficients characterizing the influence of neighbors on different elements are subjected to independent noise sources, and 2) when the coupling coefficients for all the network elements are modulated by the same stochastic signal. Without noise, the ring of chaotic maps exhibits a chimera state. The impact of noisemodulated coupling between the ring elements is explored when the parameter, which controls the correlation time and the spectral width of colored noise, and the noise intensity are varied. We investigate how the spatio-temporal structures observed in the ring evolve as the noise parameters change. The numerical results obtained are used to construct regime diagrams for the two cases of noise modulation. Our findings show the possibility of controlling the spatial structures in the ring in the presence of noise. Depending on the type of noise modulation, the spectral properties and intensity of colored noise, one can suppress the incoherent clusters of chimera states, and induce the regime of solitary states or synchronize chaotic oscillations of all the ring elements.

We study numerically external synchronization of chimera states in a network of many unidirectionally coupled layers, each representing a ring of nonlocally coupled discretetime systems. The dynamics of each element in the network is described by either the logistic map or the bistable cubic map. We consider two cases: when all $M$ unidirectionally coupled layers are identical and when $(M - 1)$ identical layers differ from the first driving layer in their nonlocal coupling parameters. It is shown that the master chimera state in the first layer can be retranslating along the network with small distortions which are defined by a parameter mismatch. We also analyze the dependence of the mean-square deviation of the structure in the ith layer on the nonlocal coupling parameters.

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.

In this paper we summarize and substantiate the relative metric entropy approach introduced in our previous papers [1,2]. Using this approach we study the mixing influence of noise on both regular and chaotic systems. We show that the synchronization phenomenon as well as stochastic resonance decrease, the degree of mixing is caused by white Gaussian noise.