Chaotic States Induced By Resetting Process In Izhikevich Neuron Model

Abstract Several hybrid neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process after spiking, have been proposed as a simple transition scheme for membrane potential between spike and hyperpolarization. As one of the hybrid spiking neuron models, Izhikevich neuron model can reproduce major spike patterns observed in the cerebral cortex only by tuning a few parameters and also exhibit chaotic states in specific conditions. However, there are a few studies concerning the chaotic states over a large range of parameters due to the difficulty of dealing with the state dependent jump on the resetting process in this model. In this study, we examine the dependence of the system behavior on the resetting parameters by using Lyapunov exponent with saltation matrix and Poincaré section methods, and classify the routes to chaos.

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Accelerating Event-Driven Simulation of Spiking Neurons with Multiple Synaptic Time Constants

Neural Computation ◽

10.1162/neco.2008.02-08-707 ◽

2009 ◽

Vol 21 (4) ◽

pp. 1068-1099 ◽

Cited By ~ 12

Author(s):

Michiel D'Haene ◽

Benjamin Schrauwen ◽

Jan Van Campenhout ◽

Dirk Stroobandt

Keyword(s):

Neuron Model ◽

Driving Forces ◽

Firing Time ◽

State Variables ◽

Neuron Models ◽

Time Constants ◽

Simulation Speed ◽

Event Driven ◽

Spiking Neuron Models ◽

Algorithmic Techniques

The simulation of spiking neural networks (SNNs) is known to be a very time-consuming task. This limits the size of SNN that can be simulated in reasonable time or forces users to overly limit the complexity of the neuron models. This is one of the driving forces behind much of the recent research on event-driven simulation strategies. Although event-driven simulation allows precise and efficient simulation of certain spiking neuron models, it is not straightforward to generalize the technique to more complex neuron models, mostly because the firing time of these neuron models is computationally expensive to evaluate. Most solutions proposed in literature concentrate on algorithms that can solve this problem efficiently. However, these solutions do not scale well when more state variables are involved in the neuron model, which is, for example, the case when multiple synaptic time constants for each neuron are used. In this letter, we show that an exact prediction of the firing time is not required in order to guarantee exact simulation results. Several techniques are presented that try to do the least possible amount of work to predict the firing times. We propose an elegant algorithm for the simulation of leaky integrate-and-fire (LIF) neurons with an arbitrary number of (unconstrained) synaptic time constants, which is able to combine these algorithmic techniques efficiently, resulting in very high simulation speed. Moreover, our algorithm is highly independent of the complexity (i.e., number of synaptic time constants) of the underlying neuron model.

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Self-Evolutionary Neuron Model for Fast-Response Spiking Neural Networks

10.36227/techrxiv.11389968.v2 ◽

2022 ◽

Author(s):

Anguo Zhang ◽

Ying Han ◽

Jing Hu ◽

Yuzhen Niu ◽

Yueming Gao ◽

...

Keyword(s):

Neuron Model ◽

Response Speed ◽

Fast Response ◽

Spiking Neural Networks ◽

Spiking Neural Network ◽

Spiking Neuron ◽

Firing Activity ◽

Neuron Models ◽

Spiking Neuron Models ◽

Classification Tasks

We propose two simple and effective spiking neuron models to improve the response time of the conventional spiking neural network. The proposed neuron models adaptively tune the presynaptic input current depending on the input received from its presynapses and subsequent neuron firing events. We analyze and derive the firing activity homeostatic convergence of the proposed models. We experimentally verify and compare the models on MNIST handwritten digits and FashionMNIST classification tasks. We show that the proposed neuron models significantly increase the response speed to the input signal.

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Relation Between Firing Statistics of Spiking Neuron with Instantaneous Feedback and Without Feedback

Fluctuation and Noise Letters ◽

10.1142/s0219477515500340 ◽

2015 ◽

Vol 14 (04) ◽

pp. 1550034 ◽

Cited By ~ 2

Author(s):

Alexander Vidybida

Keyword(s):

Neuron Model ◽

Probability Density Functions ◽

Density Functions ◽

Spiking Neuron ◽

Interspike Intervals ◽

Neuron Models ◽

Similar Relation ◽

Artificial Neurons ◽

Poisson Stream ◽

Spiking Neuron Models

We consider a class of spiking neuron models, defined by a set of conditions which are typical for basic threshold-type models like leaky integrate-and-fire, or binding neuron model and also for some artificial neurons. A neuron is fed with a point renewal process. A relation between the three probability density functions (PDF): (i) PDF of input interspike intervals ISIs, (ii) PDF of output interspike intervals of a neuron with a feedback and (iii) PDF for that same neuron without feedback is derived. This allows to calculate any one of the three PDFs provided the remaining two are given. Similar relation between corresponding means and variances is derived. The relations are checked exactly for the binding neuron model stimulated with Poisson stream.

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Qualitative Analysis of a Quadratic Integrate-and-Fire Neuron Model with State-Dependent Feedback Control

Discrete Dynamics in Nature and Society ◽

10.1155/2015/836402 ◽

2015 ◽

Vol 2015 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Guangyao Tang ◽

Jin Yang ◽

Sanyi Tang

Keyword(s):

Periodic Solution ◽

Qualitative Analysis ◽

Phase Portraits ◽

Neuron Models ◽

Integrate And Fire ◽

State Dependent ◽

Proposed Model ◽

Existence And Stability ◽

Spiking Neuron Models ◽

Important Significance

Spiking neuron models which exhibit rich dynamics are usually defined by hybrid dynamical systems. It is revealed that mathematical analysis of these models has important significance. Therefore, in this work, we provide a comprehensively qualitative analysis for a quadratic integrate-and-fire model by using the theories of hybrid dynamical system. Firstly, the exact impulsive and phase sets are defined according to the phase portraits of the proposed model, and then the Poincaré map is constructed. Furthermore, the conditions for the existence and stability of an order 1 periodic solution are provided. Moreover, the existence and nonexistence of an orderk k≥2periodic solution have been studied theoretically and numerically, and the results show that the system has periodic solutions with any period. Finally, some biological implications of the mathematical results are discussed.

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Spiking Neuron Models

10.1017/cbo9780511815706 ◽

2002 ◽

Cited By ~ 1946

Author(s):

Wulfram Gerstner ◽

Werner M. Kistler

Keyword(s):

Spiking Neuron ◽

Neuron Models ◽

Spiking Neuron Models

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Spiking neuron models

Physics Subject Headings (PhySH) ◽

10.29172/9829c04556154cdfbfc743d62381ebca ◽

2018 ◽

Keyword(s):

Spiking Neuron ◽

Neuron Models ◽

Spiking Neuron Models

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A Discrete Huber-braun Neuron Model: From Nodal Properties to Network Performance

10.21203/rs.3.rs-243100/v1 ◽

2021 ◽

Author(s):

Shaoba He ◽

Karthikeyan Rajagopal ◽

Anitha Karthikeyan ◽

Ashokkumar Sriniva

Keyword(s):

Wave Propagation ◽

Network Performance ◽

Neuron Model ◽

Coupling Effect ◽

Single Layer ◽

Simple Wave ◽

Spiral Waves ◽

Neuron Models ◽

Positive Role ◽

Multiple Wave

Abstract Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it’s the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered noise and obstacles as the two important factor which changes the excitability of the neurons in the network. When there is no noise or obstacle, the network display simple wave propagation with highly excitable neurons. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. Now when we consider only noise with no obstacle, for selected noise variances the network supports wave re-entry. By introducing an obstacle in this noisy network, the re-entry soon disappears, and the network soon enters idle state with no resetting. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. This in a two-layer network stimulus play an important role in spatiotemporal dynamics of the network. Similar noise effects like the single layer network are also seen in the two-layer network.

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