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Strange Fractal Attractors and Optimal Chaos of Memristor–Memcapacitor via Non-local Differentials

  • Kashif Ali Abro [1] ; Ambreen Siyal [2] ; Abdon Atangana [3]
    1. [1] University of the Free State

      University of the Free State

      Mangaung, Sudáfrica

    2. [2] Mehran University of Engineering and Technology

      Mehran University of Engineering and Technology

      Pakistán

    3. [3] China Medical University Hospital

      China Medical University Hospital

      Taiwán

    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 4, 2023
  • Idioma: inglés
  • Enlaces
  • Resumen

    • The multi-dimensional electronic devices are so called memory circuit elements (memristor or memcapacitor); such memory circuit elements usually rely on previous applied voltage, current, flux or charge based on memory capability with their resistance, capacitance or inductance. In view of above fact, this manuscript investigates the non-integer modeling of memristor–memcapacitor in discrete-time domain through non-singular kernels of fractal fractional differentials and integrals operators. The governing equations of memristor–memcapacitor have been developed for the sake of the dynamical characteristics of simple chaotic circuit. The fractal fractional differentials and integrals operators have been invoked for non-integer modeling of memristor–memcapacitor that can exhibit a combination of dynamical chaotic phenomena. The numerical schemes, numerical simulations, stability analysis and equilibrium points have been highlighted in detail. The comparative chaotic graphs have been discussed in three ways (i) by keeping fractal component fixed and varying fractional component distinctly, (ii) by keeping fractional component fixed and varying fractal component distinctly and (iii) by varying both fractal component and fractional component distinctly. Our results suggest that fractal-fractional model of memristor–memcapacitor retains the memory characteristics.

  • Referencias bibliográficas
    • 1. Prodromakis, T., Toumazou, C., Chua, L.: Two centuries of memristors. Nat. Mater. 11(6), 478–481 (2012)
    • 2. Chua, L.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)
    • 3. Chua, L.: Device modeling via nonlinear circuit elements. IEEE Trans. Circuits Syst. 27(11), 1014–1044 (1980)
    • 4. Ventra, M.D., Pershin, Y.V., Chua, L.O.: Circuit elements with memory: memristors-memcapacitors, and meminductors. Proc. IEEE 97(10), 1717–1724...
    • 5. Pershin, Y.V., Ventra, M.D.: Memristive circuits simulate memcapacitors and meminductors. Electron. Lett. 46(7), 517–518 (2010)
    • 6. Wu, J., Wang, L., Chen, G., Duan, S.: A memristive chaotic system with heart-shaped attractors and its implementation, Chaos solitons fractals...
    • 7. Xu, B., Wang, G., Shen, Y.: A simple meminductor-based chaotic system with complicated dynamics. Nonlinear Dyn. 88(3), 2071–2089 (2017)
    • 8. Ye, X., Mou, J., Luo, C., Yang, F., Cao, Y.: Complexity analysis of a mixed-memristors chaotic circuit. Complexity (2018). https://doi.org/10.1155/2018/8639470
    • 9. Nariman, A.K., Lobna, A.S., Ahmed, G.R., Ahmed, M.S.: General fractional order mem-elements mutators. Microelectron. J. 90, 211–221 (2019)
    • 10. Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods...
    • 11. Awan, A.U., Riaz, S., Sattar, S., Kashif, A.A.: Fractional modeling and synchronization of ferrouid on free convection flow with magnetolysis....
    • 12. Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1, 1–13 (2015)
    • 13. Kashif, A., A, Abdon, A.: Simulation and dynamical analysis of a chaotic chameleon system designed for an electronic circuit. J. Comput....
    • 14. Atangana, A., Owolabi, K.M.: New numerical approach for fractional differential equations. Math. Model. Nat. Phenom 13, 3–16 (2018)
    • 15. Abdon, A.: Extension of rate of change concept: From local to nonlocal operators with applications. Res. Phys. (2020). https://doi.org/10.1016/j.rinp.2020.103515
    • 16. Behzad, G., Gómez-Aguilar, J.F.: Two efficient numerical schemes for simulating dynamical systems and capturing chaotic behaviors with...
    • 17. Rajagopal, K., Laarem, G., Anitha, K., Ashokkumar, S., Girma, A.: Fractional order memristor no equilibrium chaotic system with its adaptive...
    • 18. Pu, Y.F., Yuan, X.: Fracmemristor: fractional-order memristor. IEEE Access 4, 1872–1888 (2016)
    • 19. Liu, H., Yang, J.: Sliding-mode synchronization control for uncertain fractional-order chaotic systems with time delay. Entropy 17(6),...
    • 20. Kashif, A.A., Jose, F.G.A.: Fractional modeling of fin on non-Fourier heat conduction via modern fractional differential operators. Arab....
    • 21. Seda, I.A.: Numerical analysis of a new Volterra integro-differential equation involving fractalfractional operators. Chaos Solit. Fract....
    • 22. Kashif, A.A.: Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators....
    • 23. Saad, K.M., Gomez-Aguilar, J.F., Almadiy, A.A.: A fractional numerical study on a chronic hepatitis C virus infection model with immune...
    • 24. Samia, R., Muhammad, A., Imran, Q.M., Qasim, A., Kashif, A.A.: A comparative study for solidification of nanoparticles suspended in nanofluids...
    • 25. Atangana, A., Goufo, E.F.D.: The Caputo-Fabrizio fractional derivative applied to a singular perturbation problem. Int. J. Math. Model....
    • 26. Maryam, A.O., Basma, S., Imran, Q.M., Kashif, A., Huda, A.: Heat transfer and fluid circulation of thermoelectric fluid through the fractional...
    • 27. Aliyu, A.I., Inc, M., Yusuf, A., Baleanu, D.: A fractional model of vertical transmission and cure of vector-borne diseases pertaining...
    • 28. Abro, K.A.: Fractional characterization of fluid and synergistic effects of free convective flow in circular pipe through Hankel transform....
    • 29. Saad, K.M., Khader, M.M., Gómez-Aguilar, J.F., Baleanu, D.: Numerical solutions of the fractional Fisher’s type equations with Atangana-Baleanu...
    • 30. Muhammad, A., Qasim, A., Kashif, A.A., Ali, R.: Characterization nanoparticles via newtonian heating for fractionalized hybrid nanofluid...
    • 31. Wen, C., Hongguang, S., Xiaodi, Z., Dean, K.: Anomalous diffusion modeling by fractal and fractional derivatives. Comput. Math. Appl....
    • 32. Abro, K.A., Atangana, A., Gomez-Aguilar, J.F.: Optimal synchronization of fractal-fractional differentials on chaotic convection for Newtonian...
    • 33. Wen, C., Yingjie, L.: New methodologies in fractional and fractal derivatives modeling. Chaos, Solitons Fractals 102, 72–77 (2017)
    • 34. Kashif, A.A., Ambreen, S., Basma, S., Abdon, A.: Application of statistical method on thermal resistance and conductance during magnetization...
    • 35. Abdon, A., Muhammad, A.K.: Validity of fractal derivative to capturing chaotic attractors. Chaos Solitons Fractals 126, 50–59 (2019)
    • 36. Sikandar, A., Khadija, Q., Kashif, A.A., Masroor, A., Imran, N.U.: Parametric study of adsorption column for arsenic removal on the basis...
    • 37. Ilknur, K.: Modeling the heat flow equation with fractional-fractal differentiation. Chaos Solitons Fractals 128, 83–91 (2019)
    • 38. Kashif, A.A., Bhagwan, D.: A scientific report of non-singular techniques on microring resonators: an application to optical technology....
    • 39. Heydari, M.H.: Numerical solution of nonlinear 2D optimal control problems generated by AtanganaRiemann-Liouville fractal-fractional derivative....
    • 40. Memon, I.Q., Abro, K.A., Solangi, M.A., Shaikh, A.A.: Thermal optimization and magnetization of nanofluid under shape effects of nanoparticles....
    • 41. Kashif, A.A., Abdon, A.: Numerical study and chaotic analysis of meminductor and memcapacitor through fractal-fractional differential...
    • 42. Abro, K.A., Atangana, A.: Simulation and dynamical analysis of a chaotic chameleon system designed for an electronic circuit. J. Comput....
    • 43. Abdon, A., Gomez-Aguilar, J.F.: Fractional derivatives with no-index law property: application to chaos and statistics. Chaos Solitons...
    • 44. Abro, K.A., Abdon, A.: Mathematical analysis of memristor through fractal-fractional differential operators: a numerical study. Math....
    • 45. Abdon, A., Gomez-Aguilar, J.F.: Decolonisation of fractional calculus rules: breaking commutativity and associativity to capture more...
    • 46. Gomez-Aguilar, J.F., Torres, L., Yepez-Martinez, H., Baleanu, D., Reyes, J.M., Sosa, I.O.: Fractional Liénard type model of a pipeline...
    • 47. Abro, K.A., Siyal, A., Atangana, A., Al-Mdallal, Q.M.: Analytical solution for the dynamics and optimization of fractional Klein-Gordon...
    • 48. Gomez-Aguilar, J.F.: Chaos and multiple attractors in a fractal-fractional Shinriki’s oscillator model. Physica A 539, 122918 (2020)
    • 49. Kashif, A.A.: A fractional and analytic investigation of thermo-diffusion process on free convection flow: an application to surface modification...
    • 50. Atangana, A.: Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex...
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