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.

Chimera resonance in networks of chaotic maps.

We explore numerically the impact of additive Gaussian noise on the spatiotemporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the Henon map. 2D distributions of the probability of observing chimera states are constructed in terms of the coupling strength and the noise intensity and for several choices of the local dynamics parameters.

Role of coupling delay in oscillatory activity in autonomous networks of excitable neurons with dissipation.

We study numerically effects of time delay in networks of delay-coupled excitable FitzHugh-Nagumo systems with dissipation. Generation of periodic self-sustained oscillations and its threshold are analyzed depending on the dissipation of a single neuron, the delay time, and random initial conditions. The peculiarities of spatiotemporal dynamics of time-delayed bidirectional ring-structured FitzHugh-Nagumo neuronal systems are investigated in cases of local and nonlocal coupling topology between the nodes, and a first-order nonequilibrium phase transition to synchrony is established.

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.

Response of solitary states to noise-modulated parameters in nonlocally coupled networks of Lozi maps.

We study numerically the impact of heterogeneity in parameters on the dynamics of nonlocally coupled discrete-time systems, which exhibit solitary states along the transition from coherence to incoherence. These partial synchronization patterns are described as states when single or several elements demonstrate different dynamics compared with the behavior of other elements in a network. Using as an example a ring network of nonlocally coupled Lozi maps, we explore the robustness of solitary states to heterogeneity in parameters of local dynamics or coupling strength.