Dynamics of a neuron exposed to integer- and fractional-order discontinuous externalmagnetic flux

Karthikeyan RAJAGOPAL, Fahimeh NAZARIMEHR, Anitha KARTHIKEYAN, Ahmed ALSAEDI, Tasawar HAYAT, Viet-Thanh PHAM

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Front. Inform. Technol. Electron. Eng ›› 2019, Vol. 20 ›› Issue (4) : 584-590. DOI: 10.1631/FITEE.1800389
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Dynamics of a neuron exposed to integer- and fractional-order discontinuous externalmagnetic flux

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Abstract

We propose a modified Fitzhugh-Nagumo neuron (MFNN) model. Based on this model, an integerorder MFNN system (case A) and a fractional-order MFNN system (case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractionalorder magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.

Keywords

Fitzhugh-Nagumo / Chaos / Fractional order / Magnetic flux

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Karthikeyan RAJAGOPAL, Fahimeh NAZARIMEHR, Anitha KARTHIKEYAN, Ahmed ALSAEDI, Tasawar HAYAT, Viet-Thanh PHAM. Dynamics of a neuron exposed to integer- and fractional-order discontinuous externalmagnetic flux. Front. Inform. Technol. Electron. Eng, 2019, 20(4): 584‒590 https://doi.org/10.1631/FITEE.1800389

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2019 Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature
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