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.The FitzHugh-Nagumo system is a paradigmatic model which describes the excitability and spiking behavior of neurons. It has various applications ranging from biological processes to nonlinear electronic circuits. In the excitable regime under the influence of noise, this model exhibits the counterintuitive phenomenon of coherence resonance. It means that there exists an optimum intermediate value of the noise intensity for which noise-induced oscillations become most regular. We investigate coherence resonance in a network of delaycoupled FitzHugh-Nagumo elements with local, nonlocal and global coupling topologies. Networks with nonlocal topology are inspired by neuroscience, as they emulate the observation that strong interconnections between neurons are typical within a certain range while fewer connections exist at longer distances. We illustrate that the interaction between the network topology, the time-delay in the coupling, and the noise leads to a rich oscillatory dynamics. In particular, we demonstrate that the regularity of this dynamics is controllable, i.e., one can enhance or weaken coherence resonance by varying the coupling and delay time.

Despite intensive research, the mechanisms underlying the neural code remain poorly understood. Recent work has focused on the response of a single neuron to a weak, sub-threshold periodic signal. By simulating the stochastic FitzHugh-Nagumo (FHN) model and then using a symbolic method to analyze the firing activity, preferred and infrequent spike patterns (defined by the relative timing of the spikes) were detected, whose probabilities encode information about the signal. As not individual neurons but neuronal populations are responsible for sensory coding and information transfer, a relevant question is how a second neuron, which does not perceive the signal, affects the detection and the encoding of the signal, done by the first neuron. Through simulations of two stochastic FHN neurons we show that the encoding of a sub-threshold signal in symbolic spike patterns is a plausible mechanism. The neuron that perceives the signal fires a spike train that, despite having an almost random temporal structure, has preferred and infrequent patterns which carry information about the signal. Our findings could be relevant for sensory systems composed by two noisy neurons, when only one detects a weak external input.

The biophysical mechanisms by which an input signal elicits a neuronal response are well known (sufficiently large inputs change the membrane potential of the neuron and generate electrical pulses, known as action potentials or spikes), yet, a good understanding of how neurons use these spikes to encode the signal information remains elusive. Recent theoretical studies have focused on how neurons encode a weak periodic signal (that by itself is unable to generate spikes) in a noisy environment, where stochastic electrical fluctuations that do not encode any information occur. Analyzing spike sequences generated by individual neurons and by two coupled neurons (that were simulated with the stochastic FitzHugh-Nagumo model), it has been found that the relative timing of the spikes can encode the signal information. Using a symbolic method to analyze the spike sequence, preferred and infrequent spike patterns were detected, whose probabilities vary with both, the amplitude and the frequency of the signal. To investigate if this encoding mechanism is plausible also for neuronal ensembles, here we analyze the activity of a group of neurons, when they all perceive a weak periodic signal. We find that, as in the case of one or two coupled neurons, the probabilities of the spike patterns, now computed from the spike sequences of all the neurons, depend on the signal's amplitude and period, and thus, the patterns' probabilities encode the information of the * Corresponding author

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Neurons encode and transmit information in spike sequences. However, despite the effort devoted to quantify their information content, little progress has been made in this regard. Here we use a nonlinear method of time-series analysis (known as ordinal analysis) to compare the statistics of spike sequences generated by applying an input signal to the neuronal model of Morris-Lecar. In particular we consider two different regimes for the neurons which lead to two classes of excitability: class I, where the frequency-current curve is continuous and class II, where the frequency-current curve is discontinuous. By applying ordinal analysis to sequences of inter-spike-intervals (ISIs) our goals are (1) to investigate if different neuron types can generate spike sequences which have similar symbolic properties; (2) to get deeper understanding on the effects that electrical (diffusive) and excitatory chemical (i.e., excitatory synapse) couplings have; and (3) to compare, when a small-amplitude periodic signal is applied to one of the neurons, how the signal features (amplitude and frequency) are encoded and transmitted in the generated ISI sequences for both class I and class II type neurons and electrical or chemical couplings. We find that depending on the frequency, specific combinations of neuron/class and coupling-type allow a more effective encoding, or a more effective transmission of the signal. a) ElectronicSensory neurons detect, encode and transmit information of external temporal stimuli (input signals such as visual, auditory, olfactory, etc.) in sequences of spikes, also known as action potentials. Despite decades of effort to understand how information is processed, the underlying mechanisms of neuronal encoding are still not fully understood. Different coding mechanisms have been proposed in the literature, which can be more or less effective depending on the level of environmental noise, the level of the external signal, and its frequency. Here we focus on the encoding of a small-amplitude periodic signal. We use a well-known neuron model to investigate the role of the excitability class of the neurons (either class I or class II) and of the type of coupling (electrical or chemical) to a second neuron that does not perceive the external signal. We find that the neuron can encode the signal in the form of preferred (more expressed) temporal spike patterns, regardless of the class of neuron and of the type of coupling. On the contrary, depending on the signal frequency, specific combinations of neuron-class and coupling-type allow a more effective encoding, or a more effective transmission of the signal.