Dynamics and implementation techniques of fractional-order neuron models: a survey

Dar, Mohammad Rafiq; Kant, Nasir Ali; Khanday, Farooq Ahmad

doi:10.1016/b978-0-12-824293-3.00017-x

Cited by 7 publications

(2 citation statements)

References 66 publications

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“…The fractional order (FO) calculus has a very long mathematical history and has gained extensive attention in the areas of science and engineering with the advent of high computational devices recent years. The FO calculus can be seen as the comprehensive and generalized version of the conventional integer-order calculus, which encompassed both fractional and integer-order differential and integral equations (Dar et al, 2022 ). Correspondingly, the FO derivative possesses complex or real arbitrary order, for which various mathematical operators have been proposed.…”

Section: Preliminary Knowledgementioning

confidence: 99%

Learning-based sliding mode synchronization for fractional-order Hindmarsh-Rose neuronal models with deterministic learning

Chen,

Li,

Yuan

et al. 2023

Front. Neurosci.

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IntroductionIn recent years, extensive research has been conducted on the synchronous behavior of neural networks. It is found that the synchronization ability of neurons is related to the performance of signal reception and transmission between neurons, which in turn affects the function of the organism. However, most of the existing synchronization methods are faced with two difficulties, one is the structural parameter dependency, which limits the promotion and application of synchronous methods in practical problems. The other is the limited adaptability, that is, even when faced with the same control tasks, for most of the existing control methods, the control parameters still need to be retrained. To this end, the present study investigates the synchronization problem of the fractional-order HindmarshRose (FOHR) neuronal models in unknown dynamic environment.MethodsInspired by the human experience of knowledge acquiring, memorizing, and application, a learning-based sliding mode control algorithm is proposed by using the deterministic learning (DL) mechanism. Firstly, the unknown dynamics of the FOHR system under unknown dynamic environment is locally accurately identified and stored in the form of constant weight neural networks through deterministic learning without dependency of the system parameters. Then, based on the identified and stored system dynamics, the model-based and relearning-based sliding mode controller are designed for similar as well as new synchronization tasks, respectively.ResultsThe synchronization process can be started quickly by recalling the empirical dynamics of neurons. Therefore, fast synchronization effect is achieved by reducing the online computing time. In addition, because of the convergence of the identification and synchronization process, the control experience can be constantly replenished and stored for reutilization, so as to improve the synchronization speed and accuracy continuously.DiscussionThe thought of this article will also bring inspiration to the related research in other fields.

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Section: Preliminary Knowledgementioning

confidence: 99%

Learning-based sliding mode synchronization for fractional-order Hindmarsh-Rose neuronal models with deterministic learning

Chen,

Li,

Yuan

et al. 2023

Front. Neurosci.

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“…Izhikevich artificial mathematical models have been proven to be an efficient model of diverse neuron responses [9]. Therefore, an aggregation of several Izhikevich artificial neurons is named electrophysiology-inspired approximated DNN or spiking DNNs [10,11].…”

Section: Introductionmentioning

confidence: 99%

Differential Neural Network-Based Nonparametric Identification of Eye Response to Enforced Head Motion

et al. 2022

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Dynamic motion simulators cannot provide the same stimulation of sensory systems as real motion. Hence, only a subset of human senses should be targeted. For simulators providing vestibular stimulus, an automatic bodily function of vestibular–ocular reflex (VOR) can objectively measure how accurate motion simulation is. This requires a model of ocular response to enforced accelerations, an attempt to create which is shown in this paper. The proposed model corresponds to a single-layer spiking differential neural network with its activation functions are based on the dynamic Izhikevich model of neuron dynamics. An experiment is proposed to collect training data corresponding to controlled accelerated motions that produce VOR, measured using an eye-tracking system. The effectiveness of the proposed identification is demonstrated by comparing its performance with a traditional sigmoidal identifier. The proposed model based on dynamic representations of activation functions produces a more accurate approximation of foveal motion as the estimation of mean square error confirms.

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A survey of fractional calculus applications in artificial neural networks

Joshi¹,

Bhosale

Vyawahare

2023

Artif Intell Rev

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Dynamics and implementation techniques of fractional-order neuron models: a survey

Cited by 7 publications

References 66 publications

Learning-based sliding mode synchronization for fractional-order Hindmarsh-Rose neuronal models with deterministic learning

Learning-based sliding mode synchronization for fractional-order Hindmarsh-Rose neuronal models with deterministic learning

Differential Neural Network-Based Nonparametric Identification of Eye Response to Enforced Head Motion

A survey of fractional calculus applications in artificial neural networks

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