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Chaos in a calcium oscillation model via Atangana-Baleanu operator with strong memory

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Abstract.

Calcium oscillations have a significant importance in gesturing messengers for a wide variety of cells because cells exhibit calcium oscillations in response to external stimulation. The significance of the calcium oscillations vividly attract researchers, this is due to the empirical, numerical or experimental analyses on calcium oscillations and the lack of modern fractional techniques. An analytic study of chaotic behavior in the calcium oscillation model is carried out through fractional and non-fractional techniques. The governing non-linear differential equations of calcium oscillations have been established through newly defined Atangana-Baleanu fractional operators. In order to analyze the dynamics of the fractional calcium oscillation model, powerful techniques are applied to the governing non-linear fractional differential equations namely the (Laplace transform and modified homotopy perturbation transform method MHATM). The newly defined Atangana-Baleanu fractional approach is examined for the parameters that show periodic doubling and route to chaos. Finally, several similarities and differences have been underlined due to the fractional-order effect for the calcium oscillations with chaotic region at different scale.

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References

  1. R. Thul, T.C. Bellamy, H.L. Roderick, M.D. Bootman, S. Coombes, Calcium oscillations, in Cellular Oscillatory Mechanisms (Springer, New York, NY, 2008)

  2. A. Atri, J. Amundson, D. Clapham, J. Sneyd, J. Biophys. 65, 1727 (1993)

    Article  Google Scholar 

  3. A. Goldbeter, Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour (Cambridge University Press, Cambridge, 1996)

  4. M. Brøns, M. Desroches, M. Krupa, Math. Popul. Stud. 22, 71 (2015)

    Article  MathSciNet  Google Scholar 

  5. M.J. Sanderson, A.C. Charles, S. Boitano, E.R. Dirksen, Mol. Cell. Endocrinol. 98, 173 (1994)

    Article  Google Scholar 

  6. J. Sneyd, A.C. Charles, M.J. Sanderson, Am. J. Physiol. 266, 293 (1994)

    Article  Google Scholar 

  7. E. Harvey, V. Kirk, M. Wechselberger, J. Sneyd, J. Nonlinear Sci. 21, 639 (2011)

    Article  ADS  Google Scholar 

  8. J.R. Weimar, Parallel Comput. 23, 1699 (1997)

    Article  MathSciNet  Google Scholar 

  9. G.B. Ermentrout, L. Edelstein-Keshet, J. Theor. Biol. 160, 97 (1993)

    Article  Google Scholar 

  10. X.-S. Yang, Appl. Math. Modell. 30, 200 (2006)

    Article  Google Scholar 

  11. T. Rüdiger, C. Stephen, R. Llewelyn, B. Martin, Proc. Natl. Acad. Sci. U.S.A. 109, 2150 (2011)

    Google Scholar 

  12. J. Latulippe, D. Lotito, D. Murby, PLoS ONE 13, 1 (2018)

    Article  Google Scholar 

  13. B. Markus, Q. Gillian, J. Math. Neurosci. 8, 9 (2018)

    Article  Google Scholar 

  14. E. Mirzakhalili, B.I. Epureanu, E. Gourgou, PLoS ONE 13, e0201302 (2018)

    Article  Google Scholar 

  15. R. Droghei, E. Salusti, J. Petrol. Sci. Eng. 125, 181 (2015)

    Article  Google Scholar 

  16. K. Ali-Abro, H. Mukarrum, M.B. Mirza, Eur. Phys. J. Plus 132, 439 (2017)

    Article  Google Scholar 

  17. M. Sheikholeslami, M. Bhatti, Int. J. Heat Mass Transfer 109, 115 (2017)

    Article  Google Scholar 

  18. K. Ali-Abro, A.A. Irfan, M.A. Sikandar, I. Khan, J. King Saud Univ., https://doi.org/10.1016/j.ksus.2018.07.012 (2018)

  19. J.F. Gómez-Aguilar, Turk. J. Electr. Eng. Comput. Sci. 24, 1421 (2016)

    Article  Google Scholar 

  20. K. Ali-Abro, A.A. Memon, M.A. Uqaili, Eur. Phys. J. Plus 133, 113 (2018)

    Article  Google Scholar 

  21. K.A. Abro, I. Khan, A. Tassadiqq, Math. Model. Nat. Phenom. 13, 1 (2018)

    Article  MathSciNet  Google Scholar 

  22. Z. Hammouch, T. Mekkaoui, Nonlinear Stud. 22, 565 (2015)

    MathSciNet  Google Scholar 

  23. K. Ali-Abro, I. Khan, J.F. Gómez-Aguilar, Eur. Phys. J. Plus 133, 397 (2018)

    Article  Google Scholar 

  24. K. Ali-Abro, M.M. Rashidi, I. Khan, I.A. Abro, A. Tassadiq, J. Nanofluids 7, 738 (2018)

    Article  Google Scholar 

  25. K. Ali-Abro, H. Mukarrum, M.B. Mirza, Prog. Fractional Differ. Appl. 3, 69 (2017)

    Article  Google Scholar 

  26. H.W. Zhoua, S. Yang, J. Hydrol. 566, 910 (2018)

    Article  ADS  Google Scholar 

  27. A. Yusuf, M. Inc, A.I. Aliyu, D. Baleanu, Chaos, Solitons Fractals 116, 220 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  28. R. Amanda, A. Atangana, Chaos, Solitons Fractals 116, 414 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  29. M.A. Khan, S. Ullah, M. Farooq, Chaos, Solitons Fractals 116, 227 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  30. K. Ali-Abro, A.D. Chandio, I.A. Abro, I. Khan, J. Therm. Anal. Calorim. 135, 2197 (2019)

    Article  Google Scholar 

  31. N.A. Sheikh, F. Ali, M. Saqib, I. Khan, S.A.A. Jan, A.S. Alshomrani, M.S. Alghamdi, Results Phys. 7, 789 (2017)

    Article  ADS  Google Scholar 

  32. J. Hristov, Therm. Sci. 21, 827 (2017)

    Article  Google Scholar 

  33. Q. Al-Mdallal, K. Ali-Abro, I. Khan, Complexity 2018, 8131329 (2018)

    Article  Google Scholar 

  34. J. Hristov, Therm. Sci. 20, 757 (2016)

    Article  Google Scholar 

  35. F. Ali, M. Saqib, I. Khan, N.A. Sheikh, Eur. Phys. J. Plus 131, 377 (2016)

    Article  Google Scholar 

  36. K. Ali-Abro, H.S. Shaikh, M. Norzieha, I. Khan, T. Asifa, Malays. J. Fundam. Appl. Sci. 14, 20 (2018)

    Google Scholar 

  37. I. Koca, A. Atangana, Therm. Sci. 21, 2299 (2017)

    Article  Google Scholar 

  38. D.M. Mugheri, K. Ali-Abro, M.A. Solangi, Int. J. Adv. Appl. Sci. 5, 97 (2018)

    Article  Google Scholar 

  39. A. Atangana, D. Baleanu, Therm. Sci. 20, 763 (2016)

    Article  Google Scholar 

  40. U. Kummer, L.F. Olsen, C.J. Dixon, A.K. Green, E. Bornberg-Bauer, G. Baier, Biophys. J. 79, 1188 (2000)

    Article  Google Scholar 

  41. Y. Suansook, K. Paithoonwattanakij, Math. Probl. Eng. 2015, 276059 (2015)

    Article  Google Scholar 

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Authors and Affiliations

  1. CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

  2. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan

    Kashif Ali Abro

  3. Department of Physics, Adeyemi College of Education, Ondo, Nigeria

    Olusola Kolebaje

  4. Department of Mathematics, Science Faculty, Ege University, Izmir, Turkey

    Ahmet Yildirim

Authors
  1. J. F. Gómez-Aguilar
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  2. Kashif Ali Abro
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  3. Olusola Kolebaje
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  4. Ahmet Yildirim
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Correspondence to J. F. Gómez-Aguilar.

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Gómez-Aguilar, J.F., Ali Abro, K., Kolebaje, O. et al. Chaos in a calcium oscillation model via Atangana-Baleanu operator with strong memory. Eur. Phys. J. Plus 134, 140 (2019). https://doi.org/10.1140/epjp/i2019-12550-1

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  • DOI: https://doi.org/10.1140/epjp/i2019-12550-1

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