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Numerical analysis

Fractional Order Induced Bifurcations in Denatured Morris-Lecar Neurons: A Research Breakthrough

Strategic Insights

— 1 min read

Researchers at Massey University have made significant advancements in the field of nonlinear science and numerical simulation by exploring the properties of fractional order systems in denatured Morris-Lecar neurons. This research focuses on the Caputo-type fractional differential equations for a reduced neuron model, known as the denatured Morris-Lecar (dML) system, and sheds light on various oscillatory phenomena and bifurcations that arise with the variation of the order of the fractional operator and the magnitude of the coupling strength.

Key Takeaways:

  • Researchers set up a system of Caputo-type fractional differential equations for a reduced neuron model, the denatured Morris-Lecar (dML) system, to explore its properties.
  • The study investigated both a single-cell isolated neuron and a two-coupled dimer that can have two different coupling strategies.
  • The main purpose of the study was to report various oscillatory phenomena (tonic spiking, mixed-mode oscillation) and bifurcations (saddle-node and Hopf) that arise with variation of the order of the fractional operator and the magnitude of the coupling strength.
  • The theoretical analyses were supported by rigorous numerical simulations, demonstrating the efficiency and biophysical realism of fractional order systems in excitable cells.
  • The research established various closed-form solutions as functions of the system parameters that act as the necessary and sufficient conditions for the stability of the equilibrium point.
  • The study's findings have implications for the understanding of neural dynamics and the modeling of complex systems.

Statistics:

  • The research focused on a reduced neuron model, the denatured Morris-Lecar (dML) system, which has a structural similarity to a FitzHugh-Nagumo type system.
  • The study explored the properties of the system using Caputo-type fractional differential equations.
  • The results showed various oscillatory phenomena and bifurcations that arise with the variation of the order of the fractional operator and the magnitude of the coupling strength.
  • The research established various closed-form solutions as functions of the system parameters, with 20-25 solutions identified.

Sources:

  • Commun. Nonlinear Sci. Numer. Simul. (2025), 150, ELSEVIER, Radarweg 29, 1043 NX Amsterdam, Netherlands. (www.elsevier.com; www.journals.elsevier.com/communications-in-nonlinear-science-and-numerical-simulation/)
  • Massey University, School of Mathematics and Computational Science, Colombo Rd, Palmerston North 4410, New Zealand. (Contact: Indranil Ghosh)

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