Controlling extreme events in neuronal networks: A single driving signal approach

TL;DR

The paper addresses extreme events in neuronal networks, modeling drive–response interactions with a single relaxation-oscillatory FitzHugh–Nagumo drive neuron to suppress EE activity across three network topologies. The authors demonstrate that EE mitigation occurs as the drive–response coupling $\gamma$ increases, via two mechanisms: phase-lock breaking in a two-neuron setup and protoevent-frequency disruption in monolayer and two-layer networks. A key finding is that driving more neurons in the response layer accelerates mitigation, reducing the required $\gamma$ for suppression. The work suggests a simple, potentially real-time strategy for mitigating epileptic-like extreme events by external driving, with extensions to other neuron models and network topologies in future work.

Abstract

We show that in a drive-response coupling framework extreme events are suppressed in the response system by the dominance of a single driving signal. We validate this approach across three distinct response network topologies, namely (i) a pair of coupled neurons, (ii) a monolayer network of N coupled neurons and (iii) a two-layer multiplex network each composed of FitzHugh-Nagumo neuronal units. The response networks inherently exhibit extreme events. Our results demonstrate that influencing just one neuron in the response network with an appropriately tuned driving signal is sufficient to control extreme events across all three configurations. In the two-neuron case, suppression of extreme events occurs due to the breaking of phase-locking between the driving neuron and the targeted response neuron. In the case of monolayer and multiplex networks, suppression of extreme events results from the disruption of protoevent frequency dynamics and a subsequent frequency decoupling of the driven neuron from the rest of the network. We also observe that when the size of the neurons in response network connected to the drive increases, the onset of control occurs earlier indicating a scaling advantage of the method.

Figures (12)

• Figure 1: Drive-response coupling configuration where a single neuron in the drive (red circle) and a neuronal network in the response system (green oval). The drive neuron exhibits spiking in the form of relaxation oscillations (red box) while the response network as a whole exhibits chaotic dynamics with EE (green box).
• Figure 2: (a) Drive neuron connected with one neuron of the two coupled response network, (b) drive neuron connected with a single neuron of the monolayer response network and (c) drive neuron connected to a single neuron in the Layer-2 (Blue connected nodes) in the multiplex FHN network. Layer-1 is composed of red nodes.
• Figure 3: The time series, phase portraits, and probability distribution plots for two coupled systems (Eq. \ref{['fhn_2c']}) are shown in the 1st, 2nd, and 3rd columns, respectively. Rows (a1-a3), (b1-b3) and (c1-c3) correspond to plots for the coupling strength $\gamma = 1.0 \times 10^{-8}$, $1.0 \times 10^{-6}$ and $1.0 \times 10^{-4}$. The blue solid line in time series and probability distribution plots corresponds to the threshold $x_{th}$.
• Figure 4: Bifurcation diagram of the two coupled systems (Eq. \ref{['fhn_2c']}) by collecting the peaks of $\bar{x}$ as a function of $\gamma$. The blue solid line indicates the threshold $x_{th}$.
• Figure 5: The 1st, 2nd, and 3rd columns depict the time series, phase portraits, and probability distribution plots of the monolayer network represented by Eq. (\ref{['fhn_nc']}), respectively. Rows (a1-a3), (b1-b3) and (c1-c3) correspond to the plots for the coupling strength $\gamma = 1.0 \times 10^{-8}$, $1.0 \times 10^{-5}$ and $1.0 \times 10^{-2}$. The blue solid line in time series and probability distribution plots corresponds to the threshold $x_{th}$.