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Complex dynamics of a neuron model with discontinuous magnetic induction and exposed to external radiation

  • Fatemeh Parastesh
  • Karthikeyan Rajagopal
  • Anitha Karthikeyan
  • Ahmed Alsaedi
  • Tasawar Hayat
  • Viet-Thanh Pham
Original Research
  • 19 Downloads

Abstract

The last two decades have seen many literatures on the mathematical and computational analysis of neuronal activities resulting in many mathematical models to describe neuron. Many of those models have described the membrane potential of a neuron in terms of the leakage current and the synaptic inputs. Only recently researchers have proposed a new neuron model based on the electromagnetic induction theorem, which considers inner magnetic fluctuation and external electromagnetic radiation as a significant missing part that can participate in neural activity. While the flux coupling of the membrane is considered equivalent to a memductance function of a memristor, standard memductance model of \(\alpha + 3\beta \phi^{2}\) has been used in the literatures, but in this paper we propose a new memductance function based on discontinuous flux coupling. Various dynamical properties of the neuron model with discontinuous flux coupling are studied and interestingly the proposed model shows hyperchaotic behavior which was not identified in the literatures. Furthermore, we consider a ring network of the proposed model and investigate whether the chimera state can emerge. The chimera state relates to the state with simultaneously coherence and incoherence in oscillatory networks and has received much attention in recent years.

Keywords

HR model Discontinuous flux Bifurcation Hyperchaos Chimera state 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Fatemeh Parastesh
    • 1
  • Karthikeyan Rajagopal
    • 2
  • Anitha Karthikeyan
    • 2
  • Ahmed Alsaedi
    • 4
  • Tasawar Hayat
    • 3
    • 4
  • Viet-Thanh Pham
    • 5
  1. 1.Biomedical Engineering DepartmentAmirkabir University of TechnologyTehranIran
  2. 2.Center for Nonlinear Dynamics, College of EngineeringDefence UniversityBishoftuEthiopia
  3. 3.Department of MathematicsQuaid-I-Azam University 45320Islamabad 44000Pakistan
  4. 4.NAAM Research GroupKing Abdulaziz UniversityJeddahSaudi Arabia
  5. 5.Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics EngineeringTon Duc Thang UniversityHo Chi Minh CityVietnam

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