Excitatory Coupling Research Articles

Novel modes of synchronization in star networks of coupled chemical oscillators.

Photochemically coupled micro-oscillators are studied experimentally and computationally in star networks to investigate the modes and mechanisms of synchronization. The micro-oscillators are catalyst-loaded beads that are placed in catalyst-free Belousov-Zhabotinsky (BZ) solutions. The properties of the photochemical coupling between the oscillators are determined by the composition of the BZ reaction mixtures, and both excitatory coupling and inhibitory coupling are studied. Synchronization of peripheral oscillators coupled through a hub oscillator is exhibited at coupling strengths leading to novel modes of synchronization of the hub with the peripheral oscillators. A theoretical analysis provides insights into the mechanism of the synchronization. The heterogeneous peripheral oscillators have different phase velocities that give rise to a phase divergence; however, the perturbation from the hub acts to realign the phases by delaying the faster oscillators more than the slower oscillators.

Diversity of neuronal activity is provided by hybrid synapses

The coexistence of electrical and chemical synaptic communication among excitatory cells has been evidenced by neuroscientists. Nevertheless, theoretical understanding of hybrid synaptic connections in diverse dynamical states of neural networks for self-organization and robustness, still has not been fully studied. Here, we present a model of neural network that includes chemical excitatory coupling in a way of small-world topology and electrical synaptic coupling among adjacent excitatory cells for excitatory population. Firstly, we use this model to investigate the effect of electrical synaptic coupling among excitatory cells on global network behavior with the goal of theoretically understanding mechanisms of generating rich firing patterns. Secondly, we further study the emergence of various firing ripple events by considering the variation of chemical synaptic inhibition and other factors, such as network densities. We found that the excitatory population has a tendency to synchronization as the weights of electrical synaptic coupling among excitatory cells are increased. Moreover, the existence of these electrical synaptic connections can cause various firing patterns of interest by slightly changing the chemical synaptic weights. Our results pave a way in the study of the dynamical mechanisms and computational significance of the contribution of mixed synapse in the neural functions.

Research on time synchronization of linear pulse-coupled oscillators model with delay in nearest neighbor wireless multi-hop networks

Time synchronicity works as a popular requirement in wireless sensor networks. Pulse-coupled oscillators similar to firefly flashing and synchronization via discrete pulse coupling are widely used in wireless sensor networks. In this article, we have studied the time synchronization with communication delay in the nearest neighbor network of distributed sensors, based on the pulse-coupled oscillators model of synchronicity achieved by biological systems. First, we present a linear pulse-coupled oscillators model with coupling delay and the model is used to analyze the wireless sensor networks synchronization with communication delay. Second, we mathematically analyze the firing behaviors in the linear pulse-coupled oscillators network using the delayed excitatory coupling and track the synchronization process of the two and multi-oscillators and obtain the synchronization conditions from the regression mapping. Finally, through the proposed model implementation in the wireless sensor networks simulation framework, we demonstrate that the multi-oscillators system can be synchronized from a random starting stage distribution under linear phase responding functions and the nearest neighbor communication. The results show that our approach can achieve clock synchronization in wireless sensor networks with delayed nearest neighbor communication.

Purinergic P2 and glutamate NMDA receptor coupling contributes to osmotically driven excitability in hypothalamic magnocellular neurosecretory neurons.

Purinergic and glutamatergic signalling pathways play a key role in regulating the activity of hypothalamic magnocellular neurosecretory neurons (MNNs). However, the precise cellular mechanisms by which ATP and glutamate act in concert to regulate osmotically driven MNN neuronal excitability remains unknown. Here, we report that ATP acts on purinergic P2 receptors in MNNs to potentiate in a Ca2+ -dependent manner extrasynaptic NMDAR function. The P2-NMDAR coupling is engaged in response to an acute hyperosmotic stimulation, contributing to osmotically driven firing activity in MNNs. These results help us to better understand the precise mechanisms contributing to the osmotic regulation of firing activity and hormone release from MNNs. The firing activity of hypothalamic magnocellular neurosecretory neurons (MNNs) located in the paraventricular nucleus (PVN) and supraoptic nucleus (SON) is coordinated by the combined, fine-tuned action of intrinsic membrane properties, synaptic and extrasynaptic signalling. Among these, purinergic and glutamatergic signalling pathways have been shown to play a key role regulating the activity of MNNs. However, the precise cellular mechanisms by which ATP and glutamate act in concert to regulate osmotically driven MNN neuronal excitability remains unknown. Whole-cell patch-clamp recordings obtained from MNNs showed that ATP (100μM) induced an increase in firing rate, an effect that was blocked by either 4-[[4-formyl-5-hydroxy-6-methyl-3-[(phosphonooxy)methyl]2-pyridinyl]azo]1,3-benzenedisulfonic acid tetrasodium salt (PPADS) (10μM) or kynurenic acid (1mm). While ATP did not affect the frequency or magnitude of glutamatergic excitatory postsynaptic currents (EPSCs), it induced an inward shift in the holding current that was prevented by PPADS or kynurenic acid treatment, suggesting that ATP enhances a tonic extrasynaptic glutamatergic excitatory current. We observed that ATP-potentiated glutamatergic receptor-mediated currents were evoked by focal application of L-glu (1mm) and NMDA (50μM), but not AMPA (50μM). ATP potentiation of NMDA-evoked currents was blocked by PPADS (10μM) and by chelation of intracellular Ca2+ with BAPTA (10mm). Finally, we report that a hyperosmotic stimulus (mannitol 1%, +55mOsm/kgH2 O) potentiated NMDA-evoked currents and increased MNN firing activity, effects that were blocked by PPADS. Taken together, our data support a functional excitatory coupling between P2 and extrasynaptic NMDA receptors in MNNs, which is engaged in response to an acute hyperosmotic stimulus.

Oscillatory microcells connected on a ring by chemical waves.

The dynamics of four coupled microcells with the oscillatory Belousov-Zhabotinsky (BZ) reaction in them is analyzed with the aid of partial differential equations. Identical BZ microcells are coupled in a circle via identical narrow channels containing all the components of the BZ reaction, which is in the stationary excitable state in the channels. Spikes in the BZ microcells generate unidirectional chemical waves in the channels. A thin filter is put in between the end of the channel and the cell. To make coupling between neighboring cells of the inhibitory type, hydrophobic filters are used, which let only Br2 molecules, the inhibitor of the BZ reaction, go through the filter. To simulate excitatory coupling, we use a hypothetical filter that let only HBrO2 molecules, the activator of the BZ reaction, go through it. New dynamic modes found in the described system are compared with the "old" dynamic modes found earlier in the analogous system of the "single point" BZ oscillators coupled in a circle by pulses with time delay. The "new" and "old" dynamic modes found for inhibitory coupling match well, the only difference being much broader regions of multi-rhythmicity in the "new" dynamic modes. For the excitatory type of coupling, in addition to four symmetrical modes of the "old" type, many new asymmetrical modes coexisting with the symmetrical ones have been found. Asymmetrical modes are characterized by the spikes occurring any time within some finite time intervals.

Fine-tuning neural excitation/inhibition for tailored ketamine use in treatment-resistant depression

The glutamatergic modulator ketamine has been shown to rapidly reduce depressive symptoms in patients with treatment-resistant major depressive disorder (TRD). Although its mechanisms of action are not fully understood, changes in cortical excitation/inhibition (E/I) following ketamine administration are well documented in animal models and could represent a potential biomarker of treatment response. Here, we analyse neuromagnetic virtual electrode time series collected from the primary somatosensory cortex in 18 unmedicated patients with TRD and in an equal number of age-matched healthy controls during a somatosensory ‘airpuff’ stimulation task. These two groups were scanned as part of a clinical trial of ketamine efficacy under three conditions: (a) baseline; (b) 6–9 h following subanesthetic ketamine infusion; and (c) 6–9 h following placebo-saline infusion. We obtained estimates of E/I interaction strengths by using dynamic causal modelling (DCM) on the time series, thereby allowing us to pinpoint, under each scanning condition, where each subject’s dynamics lie within the Poincaré diagram—as defined in dynamical systems theory. We demonstrate that the Poincaré diagram offers classification capability for TRD patients, in that the further the patients’ coordinates were shifted (by virtue of ketamine) toward the stable (top-left) quadrant of the Poincaré diagram, the more their depressive symptoms improved. The same relationship was not observed by virtue of a placebo effect—thereby verifying the drug-specific nature of the results. We show that the shift in neural dynamics required for symptom improvement necessitates an increase in both excitatory and inhibitory coupling. We present accompanying MATLAB code made available in a public repository, thereby allowing for future studies to assess individually tailored treatments of TRD.

Training Spiking Neural Networks in the Strong Coupling Regime.

Recurrent neural networks trained to perform complex tasks can provide insight into the dynamic mechanism that underlies computations performed by cortical circuits. However, due to a large number of unconstrained synaptic connections, the recurrent connectivity that emerges from network training may not be biologically plausible. Therefore, it remains unknown if and how biological neural circuits implement dynamic mechanisms proposed by the models. To narrow this gap, we developed a training scheme that, in addition to achieving learning goals, respects the structural and dynamic properties of a standard cortical circuit model: strongly coupled excitatory-inhibitory spiking neural networks. By preserving the strong mean excitatory and inhibitory coupling of initial networks, we found that most of trained synapses obeyed Dale's law without additional constraints, exhibited large trial-to-trial spiking variability, and operated in inhibition-stabilized regime. We derived analytical estimates on how training and network parameters constrained the changes in mean synaptic strength during training. Our results demonstrate that training recurrent neural networks subject to strong coupling constraints can result in connectivity structure and dynamic regime relevant to cortical circuits.

Synchronization of interacted spiking neuronal networks with inhibitory coupling

• The synchronization index (SI) in two large interacted via inhibitory coupling networks oscillates periodically in time; the time intervals of high SI alternates with the time intervals of low SI. • The synchronization indexes in these networks exhibit either inphase or antiphase synchronization depending on the inhibitory coupling strength between them. We suppose that the underlying mechanism behind the antiphase dynamics lies in the cognitive resource redistribution between neuronal ensembles in the brain. • Excitatory coupling between the neurons inside the network affects the synchronization index. To maintain the neural network in the regimes of inphase or antiphase SI oscillations, we should keep a balance between excitatory and inhibitory connections. It suggests that the excitatory and the inhibitory currents should compensate each other. In other words, when one of them increases, the other must be increased too, and vice versa. • The coupling inside the input small network affects antiphase synchronization between two large networks. However, the scenario from positive and negative correlation and back between the large networks are only determined by inhibitory coupling between them. The development of mathematical models to describe neuronal interaction processes in the brain is a challenging task of nonlinear dynamics. Recent advances in biochemistry and neuroscience allow better understanding of biological mechanisms underlying the neuron functioning and synaptic connections between neurons. Moreover, significant progress in brain imaging sheds light on the structure of the brain network and certain aspects of neuronal dynamics. However, dynamical mechanisms leading to synchronization between different brain areas still remain unknown and require further investigation. To shed light on this issue, we consider two small-world networks of Hodgkin-Huxley neurons interacting via inhibitory coupling. We found that synchronization indices (SI) in both networks oscillate periodically in time, so that time intervals of high SI alternate with time intervals of low SI. Depending on the coupling strength, the two coupled networks can be in the regime of either in-phase or anti-phase synchronization. We suppose that the inherent mechanism behind such a behavior lies in the cognitive resource redistribution between neuronal ensembles of the brain.

Brain Network Simulations Indicate Effects of Neuregulin-1 Genotype on Excitation-Inhibition Balance in Cortical Dynamics.

Neuregulin-1 (NRG1) represents an important factor for multiple processes including neurodevelopment, brain functioning or cognitive functions. Evidence from animal research suggests an effect of NRG1 on the excitation-inhibition (E/I) balance in cortical circuits. However, direct evidence for the importance of NRG1 in E/I balance in humans is still lacking. In this work, we demonstrate the application of computational, biophysical network models to advance our understanding of the interaction between cortical activity observed in neuroimaging and the underlying neurobiology. We employed a biophysical neuronal model to simulate large-scale brain dynamics and to investigate the role of polymorphisms in the NRG1 gene (rs35753505, rs3924999) in n = 96 healthy adults. Our results show that G/G-carriers (rs3924999) exhibit a significant difference in global coupling (P = 0.048) and multiple parameters determining E/I-balance such as excitatory synaptic coupling (P = 0.047), local excitatory recurrence (P = 0.032) and inhibitory synaptic coupling (P = 0.028). This indicates that NRG1 may be related to excitatory recurrence or excitatory synaptic coupling potentially resulting in altered E/I-balance. Moreover, we suggest that computational modeling is a suitable tool to investigate specific biological mechanisms in health and disease.

Inhibitory autapses enhance coherence resonance of a neuronal network

The counterintuitive phenomenon that inhibitory autapses enhance coherence resonance (CR) is investigated in a Hodgkin–Huxley neuronal network, which can be well interpreted by post-inhibitory rebound (PIR) spikes. Noise can induce CR in the network with excitatory coupling. After introducing inhibitory autapses, multiple CRs induced by noise appear at multiple time delays of inhibitory autapses. The degree of CRs can be enhanced by inhibitory autapses with time delays approximating to 10 ms or the sum of 10 ms and multiples of the firing period. For these time delays, each delayed inhibitory current pulse can induce a PIR spike, which is a signature of the stable focus near the Hopf bifurcation. The degree of CRs can be reduced by inhibitory autapses for time delays nearly equaling multiples of the firing period, because the inhibitory autaptic current pulses take effect near the spikes, resulting in the reduced irregularity of the spikes. More detailed dynamics of CR is investigated in planes composed of every two parameters out of the noise intensity, the autaptic strength, and the time delay. The counterintuitive phenomenon that inhibitory autapses can enhance the CR degree is in contrast to the conventional notion that inhibitory effects suppress the neuronal activities, which not only enriches the content of nonlinear dynamics, but also provides an approach to modulate CR or the firing regularity of neuronal networks.

Stimulus classification using chimera-like states in a spiking neural network

Abstract A complex network of bistable Hodgkin-Huxley (HH) neurons with excitatory coupling can exhibit a partially spiking chimera behavior. We propose to use this chimera-like state for classification of the entering stimulus amplitude in the neural network with coexisting resting and spiking states. Due to different additive noise applied to each neuron in the network, the neurons are nonidentical. Therefore, depending on the amplitude of the external current, a part of the neurons stays in the resting state, while another part oscillates. Keeping fixed the coupling strength between neurons inside the network, we train the neural network on external pulses with two different amplitudes to adjust the coupling strength between the network neurons and two output neurons. We consider two variants of the classifier, in the presence and in the absence of inhibitory coupling between output neurons, and study how the output neurons respond to the external pulses of different amplitudes. The accuracy of the proposed classifier reaches 100% when the output neurons are inhibitory coupled, so that only one of these neurons is activated.

Flexible motor sequence generation during stereotyped escape responses.

Complex animal behaviors arise from a flexible combination of stereotyped motor primitives. Here we use the escape responses of the nematode Caenorhabditis elegans to study how a nervous system dynamically explores the action space. The initiation of the escape responses is predictable: the animal moves away from a potential threat, a mechanical or thermal stimulus. But the motor sequence and the timing that follow are variable. We report that a feedforward excitation between neurons encoding distinct motor states underlies robust motor sequence generation, while mutual inhibition between these neurons controls the flexibility of timing in a motor sequence. Electrical synapses contribute to feedforward coupling whereas glutamatergic synapses contribute to inhibition. We conclude that C. elegans generates robust and flexible motor sequences by combining an excitatory coupling and a winner-take-all operation via mutual inhibition between motor modules.

Coupling of cell fate selection model enhances DNA damage response and may underlie BE phenomenon.

Double-strand break-induced (DSB) cells send signal that induces DSBs in neighbour cells, resulting in the interaction among cells sharing the same medium. Since p53 network gives oscillatory response to DSBs, such interaction among cells could be modelled as an excitatory coupling of p53 network oscillators. This study proposes a plausible coupling model of three-mode two-dimensional oscillators, which models the p53-mediated cell fate selection in globally coupled DSB-induced cells. The coupled model consists of ATM and Wip1 proteins as variables. The coupling mechanism is realised through ATM variable via a mean-field modelling the bystander signal in the intercellular medium. Investigation of the model reveals that the coupling generates more sensitive DNA damage response by affecting cell fate selection. Additionally, the authors search for the cause-effect relationship between coupled p53 network oscillators and bystander effect (BE) endpoints. For this, they search for the possible values of uncertain parameters that may replicate BE experiments' results. At certain parametric regions, there is a correlation between the outcomes of cell fate and endpoints of BE, suggesting that the intercellular coupling of p53 network may manifest itself as the form of observed BEs.

The effects of within-neuron degree correlations in networks of spiking neurons.

We consider the effects of correlations between the in- and out-degrees of individual neurons on the dynamics of a network of neurons. By using theta neurons, we can derive a set of coupled differential equations for the expected dynamics of neurons with the same in-degree. A Gaussian copula is used to introduce correlations between a neuron's in- and out-degree, and numerical bifurcation analysis is used determine the effects of these correlations on the network's dynamics. For excitatory coupling, we find that inducing positive correlations has a similar effect to increasing the coupling strength between neurons, while for inhibitory coupling it has the opposite effect. We also determine the propensity of various two- and three-neuron motifs to occur as correlations are varied and give a plausible explanation for the observed changes in dynamics.

Synchronization transition from bursting to spiking and bifurcation mechanism of the pre-Bötzinger complex

The pre-Bötzinger complex is a neuronal network with excitatory coupling, which participates in modulation of respiratory rhythms via the generation of complex firing rhythm patterns and synchronization transitions of rhythm patterns. In the present paper, a mathematical model of single neuron that exhibits complex transition processes from bursting to spiking is selected as a unit, the network model of the pre-Bötzinger complex composed of two neurons with excitatory coupling is constructed, multiple synchronous rhythm patterns and complex transition processes of the synchronous rhythm patterns related to the biological experimental observations are simulated, and the corresponding bifurcation mechanism is acquired with the fast-slow variable dissection method. When the initial values of two neurons of the pre-Bötzinger complex are the same, with increasing the excitatory coupling strength, the theoretical model of the pre-Bötzinger complex shows complete synchronization transition processes from "fold/homoclinic" bursting, to "subHopf/subHopf" bursting, and at last to period-1 spiking. When the initial values are different, with the increases of the excitatory coupling intensity, the rhythm transition processes begin from phase synchronization behaviors including "fold/homoclinic" bursting, "fold/fold limit cycle" bursting, mixed bursting composed of "subHopf/subHopf" bursting and "fold/fold limit cycle" bursting, and "subHopf/ subHopf" bursting in sequence, and to anti-phase synchronous behavior of the period-1 spiking. The complete (in-phase) synchronous period-1 spiking for the same initial values exhibits bifurcation mechanism different from the anti-phase synchronous period-1 spiking for different initial values. The anti-phase synchronous period-1 spiking presents a novel and abnormal example of the synchronization at large excitatory coupling strength, which is different from the traditional viewpoint that large excitatory coupling often induces in-phase synchronous behavior. The results present the synchronization transition process and complex bifurcation mechanism from bursting to period-1 spiking of the pre-Bötzinger complex, and the abnormal synchronization example enriches the contents of nonlinear dynamics.

Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks.

We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which contains one excitatory-inhibitory neuron pair. The two pairs are coupled via delayed synaptic coupling between the excitatory neurons, while each inhibitory neuron is connected only to the corresponding excitatory neuron in the same population. We show that multiple equilibria can exist depending on the strength of the excitatory coupling between the populations. We conduct linear stability analysis of the equilibria and derive necessary conditions for delay-induced Hopf bifurcation. We show that these can induce two qualitatively different phase-locked behaviors, with the type of behavior determined by the sizes of the coupling delays. Numerical bifurcation analysis and simulations supplement and confirm our analytical results. Our work shows that the resting equilibrium point is unaffected by the coupling, thus the network exhibits bistability between a rest state and an oscillatory state. This may help understand how rhythms spontaneously arise in neuronal networks.

Oscillations and collective excitability in a model of stochastic neurons under excitatory and inhibitory coupling.

We study a model with excitable neurons modeled as stochastic units with three states, representing quiescence, firing, and refractoriness. The transition rates between quiescence and firing depend exponentially on the number of firing neighbors, whereas all other rates are kept constant. This model class was shown to exhibit collective oscillations (synchronization) if neurons are spiking autonomously, but not if neurons are in the excitable regime. In both cases, neurons were restricted to interact through excitatory coupling. Here we show that a plethora of collective phenomena appear if inhibitory coupling is added. Besides the usual transition between an absorbing and an active phase, the model with excitatory and inhibitory neurons can also undergo reentrant transitions to an oscillatory phase. In the mean-field description, oscillations can emerge through supercritical or subcritical Hopf bifurcations, as well as through infinite period bifurcations. The model has bistability between active and oscillating behavior, as well as collective excitability, a regime where the system can display a peak of global activity when subject to a sufficiently strong perturbation. We employ a variant of the Shinomoto-Kuramoto order parameter to characterize the phase transitions and their system-size dependence.

Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks.

Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean-field models-also known as firing rate models or firing rate equations-to account for electrical synapses. Here, we introduce a firing rate model that exactly describes the mean-field dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical synapses. The mathematical analysis of the firing rate model reveals a well-established bifurcation scenario for networks with chemical synapses, characterized by a codimension-2 cusp point and persistent states for strong recurrent excitatory coupling. The inclusion of electrical coupling generally implies neuronal synchrony by virtue of a supercritical Hopf bifurcation. This transforms the cusp scenario into a bifurcation scenario characterized by three codimension-2 points (cusp, Takens-Bogdanov, and saddle-node separatrix loop), which greatly reduces the possibility for persistent states. This is generic for heterogeneous QIF networks with both chemical and electrical couplings. Our results agree with several numerical studies on the dynamics of large networks of heterogeneous spiking neurons with electrical and chemical couplings.

Bifurcations of Time-Delay-Induced Multiple Transitions Between In-Phase and Anti-Phase Synchronizations in Neurons with Excitatory or Inhibitory Synapses

Time-delay-induced synchronous behaviors and synchronization transitions have been widely investigated for coupled neurons, and they play important roles for physiological functions. In the present study, time-delay-induced synchronized subthreshold oscillations were simulated, and the bifurcations underlying the synchronized behaviors were identified for a pair of coupled FitzHugh–Nagumo neurons. Multiple transitions between in-phase and anti-phase synchronizations induced by the time delay were simulated for the inhibitory and excitatory couplings. Subcritical or supercritical Hopf bifurcations and the stability of the Hopf-bifurcating periodic subthreshold oscillations were acquired using center manifold reduction and normal form theory. The in-phase or anti-phase synchronizations of the stable periodic subthreshold oscillations, which appear for multiple values of the time delay, were interpreted with the related eigenspace. The distributions of the different dynamical behaviors, including the synchronizations and bifurcations in the two-parameter plane of the time delay and coupling strength, were acquired for both types of synapses, and the different roles of the inhibitory and excitatory couplings on the synchronization transitions were compared.

Effects of memristor-based coupling in the ensemble of FitzHugh–Nagumo elements

In this paper, we study the impact of electrical and memristor-based couplings on some neuron-like spiking regimes, previously observed in the ensemble of two identical FitzHugh-Nagumo elements with chemical excitatory coupling. We demonstrate how increasing strength of these couplings affects on such stable periodic regimes as spiking in-phase, anti-phase and sequential activity. We show that the presence of electrical and memristor-based coupling does not essentially affect regimes of in-phase activity. Such regimes do not changes remaining stable ones. However, it is not the case for regimes of anti-phase and sequential activity. All such regimes can transform into periodic or chaotic ones which are very similar to the regimes of in-phase activity. Concerning the regimes of sequential activity, this transformation depends continuously on the coupling parameters, whereas some anti-phase regimes can disappear via a saddle-node bifurcation and nearby orbits tend to regimes of in-phase activity. Also, we show that new interesting neuron-like phenomena can appear from the regimes of sequential activity when increasing the strength of electrical and/or memristor-based coupling. The corresponding regimes can be associated with the appearance of spiral attractors containing a saddle-focus equilibrium with homoclinic orbit and, thus, they correspond to chaotic motions near the invariant manifold of synchronization, which contains all in-phase limit cycles. Such new regimes can lead to the emergence of extreme events in the system of coupled neurons. In particular, the interspike intervals can become arbitrarily large when orbit pass very close to the saddle-focus. Finally, we show that the further increase in the strength of electrical coupling and/or memristor-based coupling leads to decreasing interspike intervals and, thus, it helps to avoid such extreme behavior.