Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network

We consider a two-layer multiplex network of diffusively coupled FitzHugh-Nagumo (FHN) neurons in the excitable regime. It is shown, in contrast to SISR in a single isolated FHN neuron, that the maximum noise amplitude at which SISR occurs in the network of coupled FHN neurons is controllable, especially in the regime of strong coupling forces and long time delays. In order to use SISR in the first layer of the multiplex network to control CR in the second layer, we first choose the control parameters of the second layer in isolation such that in one case CR is poor and in another case, non-existent. It is then shown that a pronounced SISR cannot only significantly improve a poor CR, but can also induce a pronounced CR, which was non-existent in the isolated second layer. In contrast to strong intra-layer coupling forces, strong inter-layer coupling forces are found to enhance CR. While long inter-layer time delays just as long intra-layer time delays, deteriorates CR. Most importantly, we find that in a strong inter-layer coupling regime, SISR in the first layer performs better than CR in enhancing CR in the second layer. But in a weak inter-layer coupling regime, CR in the first layer performs better than SISR in enhancing CR in the second layer. Our results could find novel applications in noisy neural network dynamics and engineering

Mammalian Brain As a Network of Networks

Acknowledgements AZ, SG and AL acknowledge support from the Russian Science Foundation (16-12-00077). Authors thank T. Kuznetsova for Fig. 6.Peer reviewedPublisher PD

Coherence resonance in a network of FitzHugh-Nagumo systems: interplay of noise, time-delay and topology

We systematically investigate the phenomena of coherence resonance in time-delay coupled networks of FitzHugh-Nagumo elements in the excitable regime. Using numerical simulations, we examine the interplay of noise, time-delayed coupling and network topology in the generation of coherence resonance. In the deterministic case, we show that the delay-induced dynamics is independent of the number of nearest neighbors and the system size. In the presence of noise, we demonstrate the possibility of controlling coherence resonance by varying the time-delay and the number of nearest neighbors. For a locally coupled ring, we show that the time-delay weakens coherence resonance. For nonlocal coupling with appropriate time-delays, both enhancement and weakening of coherence resonance are possible

Mechanisms of Zero-Lag Synchronization in Cortical Motifs

Zero-lag synchronization between distant cortical areas has been observed in a diversity of experimental data sets and between many different regions of the brain. Several computational mechanisms have been proposed to account for such isochronous synchronization in the presence of long conduction delays: Of these, the phenomenon of "dynamical relaying" - a mechanism that relies on a specific network motif - has proven to be the most robust with respect to parameter mismatch and system noise. Surprisingly, despite a contrary belief in the community, the common driving motif is an unreliable means of establishing zero-lag synchrony. Although dynamical relaying has been validated in empirical and computational studies, the deeper dynamical mechanisms and comparison to dynamics on other motifs is lacking. By systematically comparing synchronization on a variety of small motifs, we establish that the presence of a single reciprocally connected pair - a "resonance pair" - plays a crucial role in disambiguating those motifs that foster zero-lag synchrony in the presence of conduction delays (such as dynamical relaying) from those that do not (such as the common driving triad). Remarkably, minor structural changes to the common driving motif that incorporate a reciprocal pair recover robust zero-lag synchrony. The findings are observed in computational models of spiking neurons, populations of spiking neurons and neural mass models, and arise whether the oscillatory systems are periodic, chaotic, noise-free or driven by stochastic inputs. The influence of the resonance pair is also robust to parameter mismatch and asymmetrical time delays amongst the elements of the motif. We call this manner of facilitating zero-lag synchrony resonance-induced synchronization, outline the conditions for its occurrence, and propose that it may be a general mechanism to promote zero-lag synchrony in the brain.Comment: 41 pages, 12 figures, and 11 supplementary figure

Macroscopic equations governing noisy spiking neuronal populations

At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely relied on heuristic partial (and partially justified) macroscopic models, which successfully reproduced a number of relevant phenomena. The relationship between these macroscopic models and the spiking noisy dynamics of the underlying cells has since then been a great endeavor. Based on recent mean-field reductions for such spiking neurons, we present here {a principled reduction of large biologically plausible neuronal networks to firing-rate models, providing a rigorous} relationship between the macroscopic activity of populations of spiking neurons and popular macroscopic models, under a few assumptions (mainly linearity of the synapses). {The reduced model we derive consists of simple, low-dimensional ordinary differential equations with} parameters and {nonlinearities derived from} the underlying properties of the cells, and in particular the noise level. {These simple reduced models are shown to reproduce accurately the dynamics of large networks in numerical simulations}. Appropriate parameters and functions are made available {online} for different models of neurons: McKean, Fitzhugh-Nagumo and Hodgkin-Huxley models

Delay-induced multistability near a global bifurcation

We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling and saddle-node bifurcations of limit cycles are found in accordance with Shilnikov's theorems.Comment: Int. J. Bif. Chaos (2007), in prin

Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions

In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate stochastic delayed integro-differential McKean-Vlasov equation that remain impenetrable, leaving the stochastic collective dynamics of such networks poorly understood. In order to study these macroscopic dynamics, we analyze networks of firing-rate neurons, i.e. with linear intrinsic dynamics and sigmoidal interactions. In that case, we prove that the solution of the mean-field equation is Gaussian, hence characterized by its two first moments, and that these two quantities satisfy a set of coupled delayed integro-differential equations. These equations are similar to usual neural field equations, and incorporate noise levels as a parameter, allowing analysis of noise-induced transitions. We identify through bifurcation analysis several qualitative transitions due to noise in the mean-field limit. In particular, stabilization of spatially homogeneous solutions, synchronized oscillations, bumps, chaotic dynamics, wave or bump splitting are exhibited and arise from static or dynamic Turing-Hopf bifurcations. These surprising phenomena allow further exploring the role of noise in the nervous system.Comment: Updated to the latest version published, and clarified the dependence in space of Brownian motion

Optimal self-induced stochastic resonance in multiplex neural networks: electrical versus chemical synapses

Electrical and chemical synapses shape the dynamics of neural networks and their functional roles in information processing have been a longstanding question in neurobiology. In this paper, we investigate the role of synapses on the optimization of the phenomenon of self-induced stochastic resonance in a delayed multiplex neural network by using analytical and numerical methods. We consider a two-layer multiplex network, in which at the intra-layer level neurons are coupled either by electrical synapses or by inhibitory chemical synapses. For each isolated layer, computations indicate that weaker electrical and chemical synaptic couplings are better optimizers of self-induced stochastic resonance. In addition, regardless of the synaptic strengths, shorter electrical synaptic delays are found to be better optimizers of the phenomenon than shorter chemical synaptic delays, while longer chemical synaptic delays are better optimizers than longer electrical synaptic delays -- in both cases, the poorer optimizers are in fact worst. It is found that electrical, inhibitory, or excitatory chemical multiplexing of the two layers having only electrical synapses at the intra-layer levels can each optimize the phenomenon. And only excitatory chemical multiplexing of the two layers having only inhibitory chemical synapses at the intra-layer levels can optimize the phenomenon. These results may guide experiments aimed at establishing or confirming the mechanism of self-induced stochastic resonance in networks of artificial neural circuits, as well as in real biological neural networks.Comment: 24 pages, 7 figure