Impact of pulse exposure on chimera state in ensemble of FitzHugh-Nagumo systems.

In this article, we consider the influence of a periodic sequence of Gaussian pulses on a chimera state in a ring of coupled FitzHugh-Nagumo systems. We found that on the way to complete spatial synchronization, one can observe a number of variations of chimera states that are not typical for the parameter range under consideration. For example, the following modes were found: breathing chimera, chimera with intermittency in the incoherent part, traveling chimera with strong intermittency, and others. For comparison, here we also consider the impact of a harmonic influence on the same chimera, and to preserve the generality of the conclusions, we compare the regimes caused by both a purely positive harmonic influence and a positive-negative one.

Controlling spatiotemporal dynamics of neural networks by Lévy noise.

We explore numerically how additive Lévy noise influences the spatiotemporal dynamics of a neural network of nonlocally coupled FitzHugh-Nagumo oscillators. Without noise, the network can exhibit various partial or cluster synchronization patterns, such as chimera and solitary states, which can also coexist in the network for certain values of the control parameters. Our studies show that these structures demonstrate different responses to additive Lévy noise and, thus, the dynamics of the neural network can be effectively controlled by varying the scale parameter and the stability index of Lévy noise. Specifically, introducing Lévy noise in the multistability mode can increase the probability of observing chimera states while suppressing solitary states. Nonetheless, decreasing the stability parameter enables one to diminish the noise effect on chimera states and amplify it on solitary states.

Classification of musical intervals by spiking neural networks: Perfect student in solfége classes.

We investigate a spike activity of a network of excitable FitzHugh-Nagumo neurons, which is under constant two-frequency auditory signals. The neurons are supplemented with linear frequency filters and nonlinear input signal converters. We show that it is possible to configure the network to recognize a specific frequency ratio (musical interval) by selecting the parameters of the neurons, input filters, and coupling between neurons. A set of appropriately configured subnetworks with different topologies and coupling strengths can serve as a classifier for musical intervals. We have found that the selective properties of the classifier are due to the presence of a specific topology of coupling between the neurons of the network.

Transition from chimera/solitary states to traveling waves.

We study numerically the spatiotemporal dynamics in a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. It is shown that the discretized oscillator exhibits richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Regimes, such as the coexistence of a multichimera state/a traveling wave and a solitary state are revealed for the first time and are studied in detail. It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient toward a purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, the observation time, initial conditions, and the influence of external noise.

Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps.

We study relay and complete synchronization in a heterogeneous triplex network of discrete-time chaotic oscillators. A relay layer and two outer layers, which are not directly coupled but interact via the relay layer, represent rings of nonlocally coupled two-dimensional maps. We consider for the first time the case when the spatiotemporal dynamics of the relay layer is completely different from that of the outer layers. Two different configurations of the triplex network are explored: when the relay layer consists of Lozi maps while the outer layers are given by Henon maps and vice versa. Phase and amplitude chimera states are observed in the uncoupled Henon map ring, while solitary state regimes are typical for the isolated Lozi map ring. We show for the first time relay synchronization of amplitude and phase chimeras, a solitary state chimera, and solitary state regimes in the outer layers. We reveal regimes of complete synchronization for the chimera structures and solitary state modes in all the three layers. We also analyze how the synchronization effects depend on the spatiotemporal dynamics of the relay layer and construct phase diagrams in the parameter plane of inter-layer vs intra-layer coupling strength of the relay layer.

Solitary states and solitary state chimera in neural networks.

We investigate solitary states and solitary state chimeras in a ring of nonlocally coupled systems represented by FitzHugh-Nagumo neurons in the oscillatory regime. We perform a systematic study of solitary states in this network. In particular, we explore the phase space structure, calculate basins of attraction, analyze the region of existence of solitary states in the system's parameter space, and investigate how the number of solitary nodes in the network depends on the coupling parameters. We report for the first time the occurrence of solitary state chimera in networks of coupled time-continuous neural systems. Our results disclose distinctive features characteristic of solitary states in the FitzHugh-Nagumo model, such as the flat mean phase velocity profile. On the other hand, we show that the mechanism of solitary states' formation in the FitzHugh-Nagumo model similar to chaotic maps and the Kuramoto model with inertia is related to the appearance of bistability in the system for certain values of coupling parameters. This indicates a general, probably a universal desynchronization scenario via solitary states in networks of very different nature.

Spiral and target wave chimeras in a 2D lattice of map-based neuron models.

We study the dynamics of a two-dimensional lattice of nonlocally coupled-map-based neuron models represented by Rulkov maps. It is firstly shown that this discrete-time neural network can exhibit spiral and target waves and corresponding chimera states when the control parameters (the coupling strength and the coupling radius) are varied. It is demonstrated that one-core, multicore, and ring-shaped core spiral chimeras can be realized in the network. We also reveal a novel type of chimera structure-a target wave chimera. We explore the transition from spiral wave chimeras to target wave structures when varying the coupling parameters. We report for the first time that the spiral wave regime can be suppressed by applying noise excitations, and the subsequent transition to the target wave mode occurs.

Forced synchronization of a multilayer heterogeneous network of chaotic maps in the chimera state mode.

We study numerically forced synchronization of a heterogeneous multilayer network in the regime of a complex spatiotemporal pattern. Retranslating the master chimera structure in a driving layer along subsequent layers is considered, and the peculiarities of forced synchronization are studied depending on the nature and degree of heterogeneity of the network, as well as on the degree of asymmetry of the inter-layer coupling. We also analyze the possibility of synchronizing all the network layers with a given accuracy when the coupling parameters are varied.