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

Masoliver, Maria; Malik, Nishant; Schöll, Eckehard; Zakharova, Anna

doi:10.1063/1.5003237

Cited by 59 publications

(48 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above definition of R T is limited to characterizing SISR in an isolated neuron. For a network of coupled neurons, SISR can be measured by redefining R T as follows (Masoliver et al, 2017 ):…”

Section: Methodsmentioning

confidence: 99%

Optimal Self-Induced Stochastic Resonance in Multiplex Neural Networks: Electrical vs. Chemical Synapses

Yamakou

Hjorth

Martens

2020

Front. Comput. Neurosci.

View full text Add to dashboard Cite

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. Additionally, 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 to the mechanism of self-induced stochastic resonance in networks of artificial neural circuits as well as in real biological neural networks.

show abstract

Section: Methodsmentioning

confidence: 99%

Optimal Self-Induced Stochastic Resonance in Multiplex Neural Networks: Electrical vs. Chemical Synapses

Yamakou

Hjorth

Martens

2020

Front. Comput. Neurosci.

View full text Add to dashboard Cite

show abstract

“…We investigate a multiplex network consisting of two layers where each layer is represented by a nonlocally coupled ring of FitzHugh-Nagumo (FHN) oscillators. This two-dimensional system is a paradigmatic model for neural excitability 45 . Previously, chimera states have been found in one-layer networks consisting of coupled oscillatory 46 and excitatory [47][48][49] FHN systems.…”

Section: Modelmentioning

confidence: 99%

Weak multiplexing in neural networks: Switching between chimera and solitary states

Mikhaylenko

Ramlow

Jalan

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

View full text Add to dashboard Cite

We investigate spatio-temporal patterns occurring in a two-layer multiplex network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the coupling between the layers is smaller than that within the layers, can have a significant impact on the dynamics of the neural network. We develop control strategies based on weak multiplexing and demonstrate how the desired state in one layer can be achieved without manipulating its parameters, but only by adjusting the other layer. We find that for coupling range mismatch weak multiplexing leads to the appearance of chimera states with different shapes of the mean velocity profile for parameter ranges where they do not exist in isolation. Moreover, we show that introducing a coupling strength mismatch between the layers can suppress chimera states with one incoherent domain (one-headed chimeras) and induce various other regimes such as in-phase synchronization or two-headed chimeras. Interestingly, small intra-layer coupling strength mismatch allows to achieve solitary states throughout the whole network.In nonlinear dynamics the paradigmatic FitzHugh-Nagumo (FHN) system is used to model the behavior of neurons. A single-layer network of nonlocally coupled oscillatory FHN neurons demonstrates various dynamic regimes including chimera states, that represent an intriguing mechanism of transition from complete coherence to complete incoherence. Here, we focus on a two-layer multiplex network and develop the tools for controlling the spatio-temporal patterns in the presence of weak coupling between the layers, i.e. weak multiplexing. We show that multiplexing combined with a mismatch between the layers, allows to induce chimera states in networks, where they do not appear in isolation. Our control also works in the opposite direction leading to the suppression of chimera states. Interestingly, small mismatch in the intra-layer coupling strength results in the formation of solitary states, that offer, compared to chimera states, an alternative scenario of transition from coherence to incoherence. Since multilayer structures naturally occur in neural networks (e.g., brain networks), we expect that our results can be useful for understanding and controlling of biological networks.

show abstract

“…The FHN neuron model (for biophysical details, see [55]) has been extensively used to investigate many complex dynamical behaviors occurring in neuroscience [56][57][58][59][60]. For our investigation of SISR, we consider the following version of the FHN neuron model written on the slow timescale τ as…”

Section: Model Equationmentioning

confidence: 99%

Coherent neural oscillations induced by weak synaptic noise

Yamakou

Jost

2018

Nonlinear Dyn

View full text Add to dashboard Cite

We analyze the effect of synaptic noise on the dynamics of the FitzHugh-Nagumo (FHN) neuron model. In our deterministic parameter regime, a limit cycle solution cannot emerge through a singular Hopf bifurcation, but such a limit cycle can nevertheless arise as a stochastic effect, as a consequence of weak synaptic noise in a regime of strong timescale separation (ε → 0) between the slow and fast variables of the model. We investigate the mechanism behind this phenomenon, known as self-induced stochastic resonance (SISR) (Muratov et al. in Physica D 210:227-240, 2005), by using multiple-time perturbation techniques and by analyzing the escape mechanism of the random trajectories from the stable manifolds of the model equation. Even though SISR occurs only in the limit as the singular parameter ε → 0, decreasing ε does not increase the coherence of the oscillations in the FHN model, but rather increases the interval of the noise amplitude σ for which coherence occurs. This is in contrast to the dynamical system studied in Mura- 2005). Moreover, the phenomenon is robust under parameter tuning. Numerical simulations exhibit the results predicted by the theoretical analysis. In fact, our analysis together with that in Yamakou and Jost (Weak noise-induced transitions with inhibition and modulation of neural oscillations, 2017) reveals that the FHN model can support different stochastic resonance phenomena. While it had been known (Pikovsky and Kurths in Phys Rev Lett 78:775-778, 1997) that coherence resonance can occur when the slow variable is subjected to noise, we show that, when noise is added to the fast variable, two other types, inverse stochastic resonance and SISR, may emerge in the same weak noise limit and that the transition between these phenomena can be induced by varying a simple parameter.

show abstract

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

Cited by 59 publications

References 41 publications

Optimal Self-Induced Stochastic Resonance in Multiplex Neural Networks: Electrical vs. Chemical Synapses

Optimal Self-Induced Stochastic Resonance in Multiplex Neural Networks: Electrical vs. Chemical Synapses

Weak multiplexing in neural networks: Switching between chimera and solitary states

Coherent neural oscillations induced by weak synaptic noise

Contact Info

Product

Resources

About