Dynamics and network behavior of a four-dimensional discrete neuron model with magnetic flux coupling

• Published in: European physical journal plus 2023-08, Vol.138 (8), p.683, Article 683
• Main Authors: Kumarasamy, Suresh, Moroz, Irene M., Sampathkumar, Sakthi Kumar, Karthikeyan, Anitha, Rajagopal, Karthikeyan
• Format: Article
• Language: English
• Subjects: Applied and Technical Physics; Atomic; Behavior; Complex Systems; Condensed Matter Physics; Coupling; Dynamical systems; Dynamics; Eigenvalues; Fluctuations; Initial conditions; Liapunov exponents; Magnetic flux; Mathematical and Computational Physics; Mathematical models; Molecular; Neural networks; Neurons; Optical and Plasma Physics; Ordinary differential equations; Parameter estimation; Parameters; Phase diagrams; Physics; Physics and Astronomy; Potassium; Regular Article; Stability analysis; Theoretical; Traveling waves
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-023-04329-y

Discrete neuron models show a rich variety of dynamics and potential in applying them to large and complex networks. In this work, we propose a four-dimensional discrete neuron model with magnetic flux coupling. We present a detailed stability analysis of the system with its fixed points and their eigenvalues. The four-dimensional neuron model shows bistability in the dynamics; we have shown this with the basin of attraction of initial conditions. The model shows various dynamical behaviors such as periodic, quasiperiodic, and chaotic dynamics. The lower value of external current I and Euler discretization step size ( h ) shows regular behavior such as periodic and quasiperiodic dynamics. While larger values of the I and h show chaotic dynamics. The dynamics of the four-dimensional discrete neuron model are evaluated with the help of phase diagrams and Lyapunov exponents. Two-parameter phase diagrams are drawn for different pairs of parameter choices using the Lyapunov exponent to segregate the different dynamics present in the system. We also investigate the rich dynamics of a complex network composed of four-dimensional Hindmarsh–Rose neurons with memristive flux coupling. The findings reveal the emergence of various phenomena such as chimera states and traveling waves, providing valuable insights into the collective behavior of the network and its potential implications for understanding complex neuronal dynamics.