Izhikevich Neuron Model Research Articles

Strange nonchaotic attractors in quasiperiodically driven Izhikevich neuron models

Evidence for the existence of a strange nonchaotic attractor (SNA) in a two-frequency quasiperiodically driven Izhikevich neuron model is presented. In this study, we found that the SNA is formed by a Heagy-Hammel mechanism because the SNA arises as Poincare sections of a period-doubled torus attractor collides with its unstable parent. Analyses of the fractal dimension, autocorrelation function, power spectral density, power spectral distribution function and interspike interval distribution function also support the existence of the SNA.

Characterization of the causality between spike trains with permutation conditional mutual information

Uncovering the causal relationship between spike train recordings from different neurons is a key issue for understanding the neural coding. This paper presents a method, called permutation conditional mutual information (PCMI), for characterizing the causality between a pair of neurons. The performance of this method is demonstrated with the spike trains generated by the Poisson point process model and the Izhikevich neuronal model, including estimation of the directionality index and detection of the temporal dynamics of the causal link. Simulations show that the PCMI method is superior to the transfer entropy and causal entropy methods at identifying the coupling direction between the spike trains. The advantages of PCMI are twofold: It is able to estimate the directionality index under the weak coupling and against the missing and extra spikes.

Bridging the gap between Computational Neuroscience and Systems Biology modelling

Bridging the gap between Computational Neuroscience and Systems Biology modelling

Identification of Dynamical States in Stimulated Izhikevich Neuron Models by Using a 0-1 Test

Identification of Dynamical States in Stimulated Izhikevich Neuron Models by Using a 0-1 Test

Dynamical behavior of multi-timescale adaptive threshold model

Computational models play a significant role in exploring novel theories to complement the findings of physiological experiments. Various computational models have been developed to reveal the mechanisms underlying brain functions. Particularly, in the development of therapies to modulate behavioral and pathological abnormalities, computational models provide the basic foundations to exhibit transitions between physiological and pathological conditions. Considering the significant roles of the intrinsic properties of the globus pallidus and the coupling connections between neurons in determining the firing patterns and the dynamical activities of the basal ganglia neuronal network, we propose a hypothesis that pathological behaviors under the Parkinsonian state may originate from combined effects of intrinsic properties of globus pallidus neurons and synaptic conductances in the whole neuronal network. In order to establish a computational efficient network model, hybrid Izhikevich neuron model is used due to its capacity of capturing the dynamical characteristics of the biological neuronal activities. Detailed analysis of the individual Izhikevich neuron model can assist in understanding the roles of model parameters, which then facilitates the establishment of the basal ganglia–thalamic network model, and contributes to a further exploration of the underlying mechanisms of the Parkinsonian state. Simulation results show that the hybrid Izhikevich neuron model is capable of capturing many of the dynamical properties of the basal ganglia–thalamic neuronal network, such as variations of the firing rates and emergence of synchronous oscillations under the Parkinsonian condition, despite the simplicity of the two-dimensional neuronal model. It may suggest that the computational efficient hybrid Izhikevich neuron model can be used to explore basal ganglia normal and abnormal functions. Especially it provides an efficient way of emulating the large-scale neuron network and potentially contributes to development of improved therapy for neurological disorders such as Parkinson's disease.

Stochastic and coherence resonance in feed-forward-loop neuronal network motifs

The relationships between noise and complex dynamic behaviors of neuronal ensembles are key questions in computational neuroscience, particularly in understanding some basic signal transmission mechanisms of the brain. Here we systemically investigate both the stochastic resonance (SR) and coherence resonance (CR) in the triple-neuron feed-forward-loop (FFL) network motifs by computational modeling. We use the Izhikevich neuron model as well as the chemical coupling to build the FFL motifs, and consider all possible motif types. The simulation results demonstrate that these motifs can exploit noise to enrich its dynamic performance. With a proper choice of noise intensities, both the SR and CR can be exhibited in many types of the FFLs. On the other hand, our results also indicate that the coupling strength serves as a control parameter, which has great impacts on the stochastic dynamics of the FFL motifs. Additionally, biological implications of presented results in the field of neuroscience are outlined.

New insights offered by a computational model of deep brain stimulation

Deep brain stimulation (DBS) is a standard neurosurgical procedure used to treat motor symptoms in about 5% of patients with Parkinson’s disease (PD). Despite the indisputable success of this procedure, the biological mechanisms underlying the clinical benefits of DBS have not yet been fully elucidated. The paper starts with a brief review on the use of DBS to treat PD symptoms. The second section introduces a computational model based on the population density approach and the Izhikevich neuron model. We explain why this model is appropriate for investigating macroscopic network effects and exploring the physiological mechanisms which respond to this treatment strategy (i.e., DBS). Finally, we present new insights into the ways this computational model may help to elucidate the dynamic network effects produced in a cerebral structure when DBS is applied.

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Phase synchronization phenomena of neuronal networks are one of many features depicted by real networks that can be studied using computational models. Here, we proceed with numerical simulations of a globally connected network composed of non-identical (distinct) Izhikevich neuron model to study clustered phase synchronization. We investigate the case in which, once coupled, there exist two main neuron clusters in the network: one of them is bi-stable, depicting phase-synchronized or unsynchronized states, depending on the initial conditions; and the second one shows just an unsynchronized state. For the set of initial conditions that lead the first cluster to the synchronized regime, we observe a chimera-like pattern of the network. For small networks, the dynamics can also present intermittent chimera-like scenarios. In this context, the mechanism for intermittent chimera states is based on two features: the coexistence of a synchronized cluster with an unsynchronized one; and the capability of one cluster to display bi-stability depending on the signal trait by which it is forced. We conclude with an understanding of intermittent chimera-like dynamics as the limit case where bi-stability is not maintained, which occurs due to the loss of uniformity in the neuron input synaptic currents.