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On-line Access: 2019-05-14

Received: 2018-06-23

Revision Accepted: 2018-09-14

Crosschecked: 2019-01-25

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Karthikeyan Rajagopal


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Frontiers of Information Technology & Electronic Engineering  2019 Vol.20 No.4 P.584-590


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

Author(s):  Karthikeyan Rajagopal, Fahimeh Nazarimehr, Anitha Karthikeyan, Ahmed Alsaedi, Tasawar Hayat, Viet-Thanh Pham

Affiliation(s):  Center for Nonlinear Dynamics, Defence University, Bishoft 6020, Ethiopia; more

Corresponding email(s):   phamvietthanh@tdt.edu.vn

Key Words:  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 external magnetic flux[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(4): 584-590.

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author="Karthikeyan Rajagopal, Fahimeh Nazarimehr, Anitha Karthikeyan, Ahmed Alsaedi, Tasawar Hayat, Viet-Thanh Pham",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Dynamics of a neuron exposed to integer- and fractional-order discontinuous external magnetic flux
%A Karthikeyan Rajagopal
%A Fahimeh Nazarimehr
%A Anitha Karthikeyan
%A Ahmed Alsaedi
%A Tasawar Hayat
%A Viet-Thanh Pham
%J Frontiers of Information Technology & Electronic Engineering
%V 20
%N 4
%P 584-590
%@ 2095-9184
%D 2019
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1800389

T1 - Dynamics of a neuron exposed to integer- and fractional-order discontinuous external magnetic flux
A1 - Karthikeyan Rajagopal
A1 - Fahimeh Nazarimehr
A1 - Anitha Karthikeyan
A1 - Ahmed Alsaedi
A1 - Tasawar Hayat
A1 - Viet-Thanh Pham
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 20
IS - 4
SP - 584
EP - 590
%@ 2095-9184
Y1 - 2019
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1800389

We propose a modified fitzhugh-Nagumo neuron (MFNN) model. Based on this model, an integer-order 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. Fractional-order 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.




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[1]Abdolmohammadi HR, Khalaf AJM, Panahi S, et al., 2018. A new 4D chaotic system with hidden attractor and its engineering applications: analog circuit design and field programmable gate array implementation. Pramana, 90(6):70.

[2]Baskonus HM, Bulut H, 2015. On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method. Open Math, 13(1):547-556.

[3]Bertsias P, Safari L, Minaei S, et al., 2018. Fractional-order differentiators and integrators with reduced circuit complexity. Int Symp on Circuits and Systems, p.1-4.

[4]Blażejczyk-Okolewska B, Kapitaniak T, 1998. Co-existing attractors of impact oscillator. Chaos Sol Fract, 9(8):1439-1443.

[5]Cafagna D, Grassi G, 2013. Elegant chaos in fractional-order system without equilibria. Math Probl Eng, Article 380436.

[6]Cafagna D, Grassi G, 2015. Fractional-order systems without equilibria: the first example of hyperchaos and its application to synchronization. Chin Phys B, 24(8):080502.

[7]Chudzik A, Perlikowski P, Stefanski A, et al., 2011. Multistability and rare attractors in van der Pol-Duffing oscillator. Int J Bifurc Chaos, 21(7):1907-1912.

[8]Dawson SP, Grebogi C, Yorke JA, et al., 1992. Antimonotonicity: inevitable reversals of period-doubling cascades. Phys Lett A, 162(3):249-254.

[9]Diethelm K, 1997. An algorithm for the numerical solution of differential equations of fractional order. Electron Trans Numer Anal, 5:1-6.

[10]Diethelm K, Ford NJ, 2002. Analysis of fractional differential equations. J Math Anal Appl, 265(2):229-248.

[11]Diethelm K, Ford NJ, Freed AD, 2004. Detailed error analysis for a fractional Adams method. Numer Algor, 36(1):31-52.

[12]Elwakil AS, 2010. Fractional-order circuits and systems: an emerging interdisciplinary research area. IEEE Circ Syst Mag, 10(4):40-50.

[13]Fitzhugh R, 1961. Impulses and physiological states in theoretical models of nerve membrane. Biophys J, 1(6):445-466.

[14]Freeman WJ, 1988. Strange attractors that govern mammalian brain dynamics shown by trajectories of electroencephalographic (EEG) potential. IEEE Trans Circ Syst, 35(7):781-783.

[15]Gu HG, Pan BB, 2015. A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model. Nonl Dynam, 81(4):2107-2126.

[16]Haghighi HS, Markazi AHD, 2017. A new description of epileptic seizures based on dynamic analysis of a thalamocortical model. Sci Rep, 7:13615.

[17]Hodgkin AL, Huxley AF, 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol, 117(4):500-544.

[18]Itoh M, Chua LO, 2008. Memristor oscillators. Int J Bifurc Chaos, 18(11):3183-3206.

[19]Izhikevich EM, 2004. Which model to use for cortical spiking neurons? IEEE Trans Neur Netw, 15(5):1063-1070.

[20]Jenson VG, Jeffreys GV, 1977. Mathematical Methods in Chemical Engineering. Elsevier, Amsterdam, the Netherlands.

[21]Kengne J, Negou AN, Tchiotsop D, 2017. Antimonotonicity, chaos and multiple attractors in a novel autonomous memristor-based jerk circuit. Nonl Dynam, 88(4):2589-2608.

[22]Li CL, Zhang J, 2016. Synchronisation of a fractional-order chaotic system using finite-time input-to-state stability. Int J Syst Sci, 47(10):2440-2448.

[23]Lv M, Wang CN, Ren GD, et al., 2016. Model of electrical activity in a neuron under magnetic flow effect. Nonl Dynam, 85(3):1479-1490.

[24]Lv M, Ma J, Yao YG, et al., 2018. Synchronization and wave propagation in neuronal network under field coupling. Sci China Technol Sci, in press.

[25]Ma J, Wang CN, Tang J, et al., 2010. Eliminate spiral wave in excitable media by using a new feasible scheme. Commun Nonl Sci Numer Simul, 15(7):1768-1776.

[26]Ma J, Wu FQ, Wang CN, 2016. Synchronization behaviors of coupled neurons under electromagnetic radiation. Int J Mod Phys B, 31(2):1650251.

[27]Ma J, Wang Y, Wang CN, et al., 2017a. Mode selection in electrical activities of myocardial cell exposed to electromagnetic radiation. Chaos Sol Fract, 99:219-225.

[28]Ma J, Wu FQ, Ren GD, et al., 2017b. A class of initials-dependent dynamical systems. Appl Math Comput, 298:65-76.

[29]Ma J, Wu FQ, Alsaedi A, et al., 2018. Crack synchronization of chaotic circuits under field coupling. Nonl Dynam, 93(4):2057-2069.

[30]McSharry PE, Smith LA, Tarassenko L, 2003. Prediction of epileptic seizures: are nonlinear methods relevant? Nat Med, 9(3):241-242.

[31]Nagumo J, Arimoto S, Yoshizawa S, 1962. An active pulse transmission line simulating nerve axon. Proc IRE, 50(10):2061-2070.

[32]Panahi S, Aram Z, Jafari S, et al., 2017. Modeling of epilepsy based on chaotic artificial neural network. Chaos Sol Fract, 105:150-156.

[33]Perc M, Rupnik M, Gosak M, et al., 2009. Prevalence of stochasticity in experimentally observed responses of pancreatic acinar cells to acetylcholine. Chaos, 19(3):037113.

[34]Pham VT, Kingni ST, Volos C, et al., 2017. A simple three-dimensional fractional-order chaotic system without equilibrium: dynamics, circuitry implementation, chaos control and synchronization. AEU Int J Electron Commun, 78:220-227.

[35]Pham VT, Volos C, Jafari S, et al., 2018. A novel cubic-equilibrium chaotic system with coexisting hidden attractors: analysis, and circuit implementation. J Circ Syst Comput, 27(4):1850066.

[36]Qian Y, Liu F, Yang KL, et al., 2017. Spatiotemporal dynamics in excitable homogeneous random networks composed of periodically self-sustained oscillation. Sci Rep, 7(1):11885.

[37]Ren GD, Zhou P, Ma J, et al., 2017. Dynamical response of electrical activities in digital neuron circuit driven by autapse. Int J Bifurc Chaos, 27:1750187.

[38]Rostami Z, Pham VT, Jafari S, et al., 2018. Taking control of initiated propagating wave in a neuronal network using magnetic radiation. Appl Math Comput, 338:141-151.

[39]Schmidt C, Grant P, Lowery M, et al., 2013. Influence of uncertainties in the material properties of brain tissue on the probabilistic volume of tissue activated. IEEE Trans Biomed Eng, 60(5):1378-1387.

[40]Shah DK, Chaurasiya RB, Vyawahare VA, et al., 2017. FPGA implementation of fractional-order chaotic systems. AEU Int J Electron Commun, 78:245-257.

[41]Stamova I, Stamov G, 2017. Functional and Impulsive Differential Equations of Fractional Order: Qualitative Analysis and Applications. CRC Press, Boca Raton, USA.

[42]Sun H, Abdelwahab A, Onaral B, 1984. Linear approximation of transfer function with a pole of fractional power. IEEE Trans Autom Contr, 29(5):441-444.

[43]Vastarouchas C, Psychalinos C, Elwakil AS, 2018. Fractional-order model of a commercial ear simulator. IEEE Int Symp on in Circuits and Systems, p.1-4.

[44]Wang CN, Lv M, Alsaedi A, et al., 2017. Synchronization stability and pattern selection in a memristive neuronal network. Chaos, 27(11):113108.

[45]Wu FQ, Wang CN, Xu Y, et al., 2016. Model of electrical activity in cardiac tissue under electromagnetic induction. Sci Rep, 6:28.

[46]Wu FQ, Wang Y, Ma J, et al., 2018. Multi-channels coupling-induced pattern transition in a tri-layer neuronal network. Phys A, 493:54-68.

[47]Wu HG, Bao BC, Liu Z, et al., 2016. Chaotic and periodic bursting phenomena in a memristive Wien-bridge oscillator. Nonl Dynam, 83(1-2):893-903.

[48]Xu Y, Jia Y, Ma J, et al., 2018. Collective responses in electrical activities of neurons under field coupling. Sci Rep, 8(1):1349.

[49]Yang SM, Wei XL, Deng B, et al., 2018. Efficient digital implementation of a conductance-based globus pallidus neuron and the dynamics analysis. Phys A, 494:484-502.

[50]Zambrano-Serrano E, Muñoz-Pacheco J, Campos-Cantón E, 2017. Chaos generation in fractional-order switched systems and its digital implementation. AEU Int J Electron Commun, 79:43-52.

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