Noise-induced cooperative dynamics and its control in coupled neuron models

We study control of synchronization in weakly coupled oscillator networks by using a phase reduction approach. Starting from a general class of limit cycle oscillators we derive a phase model, which shows that delayed feedback control changes effective coupling strengths and effective frequencies. We derive the analytical condition for critical control gain, where the phase dynamics of the oscillator becomes extremely sensitive to any perturbations. As a result the network ca...

We study the synchronization region of two unidirectionally coupled, in a master-slave configuration, FitzHugh-Nagumo systems under the influence of external forcing terms. We observe that anticipated synchronization is robust to the different types of forcings. We then use the predict-prevent control method to suppress unwanted pulses in the master system by using the information of the slave output. We find that this method is more efficient than the direct control method b...

We investigate a ring of $N$ FitzHugh--Nagumo elements coupled in \emph{phase-repulsive} fashion and submitted to a (subthreshold) common oscillatory signal and independent Gaussian white noises. This system can be regarded as a reduced version of the one studied in [Phys. Rev. E \textbf{64}, 041912 (2001)], although externally forced and submitted to noise. The noise-sustained synchronization of the system with the external signal is characterized.

Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian approximation as well as (2) a dichotomous model. The system demonstrates ordering phase transitions and multi-stability. That is, for a strong enough feedback it exhibits nontrivial stationary states and oscillatory states whose frequencies depend on...

We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling as a function of two physiologically relevant parameters: the external current input only to the first neuron and the strength of the coupling from the first to the second neuron. Leveraging a timescale separation, we prov...

Here we present a study of stochastic resonance in an extended FitzHugh-Nagumo system with a field dependent activator diffusion. We show that the system response (here measured through the output signal-to-noise ratio) is enhanced due to the particular form of the non-homogeneous coupling. Such a result supports previous ones obtained in a simpler scalar reaction-diffusion system and shows that such an enhancement, induced by the field dependent diffusion -or selective coupl...

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics w...

The impact of inhibitory and excitatory synapses in delay-coupled Hodgkin--Huxley neurons that are driven by noise is studied. If both synaptic types are used for coupling, appropriately tuned delays in the inhibition feedback induce multiple firing coherence resonances at sufficiently strong coupling strengths, thus giving rise to tongues of coherency in the corresponding delay-strength parameter plane. If only inhibitory synapses are used, however, appropriately tuned delay...

Complex systems, such as biological networks, frequently display intricate rhythmic behaviors emerging from simple, small-amplitude dynamics in individual components. This study investigates how significant oscillatory signals can arise from a minimal system comprising just two interacting units, each exhibiting simple, non-oscillatory dynamics with weak individual outputs. Contrary to the assumption that large-scale oscillations require numerous units, our model demonstrates...

In this paper, we propose a dynamic delayed feedback control approach for desynchronization of chaotic-bursting synchronous activities in an ensemble of globally coupled neuronal oscillators. We demonstrate that the difference signal between an ensemble's mean field and its time delayed state, filtered and fed back to the ensemble, can suppress the self-synchronization in the ensemble. These individual units are decoupled and stabilized at the desired desynchronized states wh...