Analysis of an Electrical Circuit Using Two-Parameter Conformable Operator in the Caputo Sense

Neuron model have been extensively studied and different models have been proposed. Nobel laureate Hodgkin-Huxley model is physiologically relevant and can demonstrate different neural behaviors, but it is mathematically complex. For this reason, simplified neuron models such as integrate-and-fire model and its derivatives are more popular in the literature to study neural populations. Lapicque’s integrate-and-fire model is proposed in 1907 and its leaky integrate-and-fire version is very popular due to its simplicity. In order to improve this simple model and capture different aspects of neurons, a variety of it have been proposed. Fractional order derivative-based neuron models are one of those varieties, which can show adaptation without necessitating additional differential equations. However, fractional-order derivatives could be computationally costly. Recently, a conformal fractional derivative (CFD) is suggested in literature. It is easy to understand and implement compared to the other methods. In this study, a CFD-based leaky integrate-and-fire neuron model is proposed. The model captures the adaptation in firing rate under sustained current injection. Results suggest that it could be used to easily and efficiently implement network models as well as to model different sensory afferents.

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Section: The Conformal Fractional Derivative and The Cfd Capacitor Modelmentioning

confidence: 99%

“…The CFD capacitors and analysis of their usage with other circuit elements have also come out as a popular topic [22,[27][28][29][30][31]. Some circuits which have been analyzed with the CFD can be found in [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

A Conformal Fractional Derivative-based Leaky Integrate-and-Fire Neuron Model

Devecioğlu

Mutlu

2022

Sakarya University Journal of Science

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“…Authors of [17] studied four passive synthesis methods for a fractal order circuit model, which described the physical significance of components better and improved the accuracy of the model. A new operator called conformable derivative in the Caputo sense was proposed in [18] and derived the solution for the two-parameter operator of a circuit containing two supercapacitors. The operator could be extended for circuits containing any number of elements.…”

Section: Introductionmentioning

confidence: 99%

Accurate Electromagnetic Force Analysis of Offshore Wind Power Transformer Windings Based on Fractional Order Lumped Parameter Model

Zhong,

Zuo,

Wang

et al. 2023

Symmetry

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Accurate calculation of the electromagnetic force distribution of transformer windings under different loads and fault conditions is of great significance for transformer maintenance, condition evaluation and life prediction. Due to the influence of offshore wind power systems, offshore wind power transformers have high harmonic content and large changes in load rates, which can easily cause the coil destabilization, winding deformation or even damage because of the uneven distribution of the electromagnetic force. To improve the accuracy of electromagnetic force calculation, this paper proposes a fractional order numerical method. First, a three-dimensional axisymmetric transformer model and a symmetrical lumped parameter equivalent circuit model are established, respectively, based on field-circuit coupling. Second, the fractional order approximation of circuit components is realized by using the improved Oustaloup filter. In the fractional order model, the transformer is replaced by the lumped parameter equivalent circuit model. Third, as in the calculation process for integer order electromagnetic force, the integer order current has a large error, and the current waveform does not match the actual power frequency. The fractional order current and electromagnetic force at the 0.9 order are closer to the rated value. Finally, the effects of different load rates, three-phase short circuits and harmonic conditions are studied with the fractional order model. Compared with the traditional integer order finite element electromagnetic model, the fractional order equivalent circuit model established in this paper is more accurate and suitable for electromagnetic force calculation. The proposed method is significant for the structural design and state detection of transformers and also could be applied in the analysis of other dry-type transformers.

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“…Piotrowska and Sajewski [9] study the problem of describing voltage dynamics in electric circuits, involving appropriate fractional-order elements in the analysis. The authors design a linear system of state equations by using the two-parameter operator conformable derivative in the Caputo sense.…”

mentioning

confidence: 99%