Dynamics and network behavior of a four-dimensional discrete neuron model with magnetic flux coupling
Centre for Computational Modeling, Chennai Institute of Technology, 600069, Chennai, India
2 Mathematical Institute, University of Oxford, Andrew Wiles Building, ROQ, OX2 6GG, Oxford, UK
3 Department of Computer Science Engineering, Chennai Institute of Technology, 600069, Chennai, India
4 Department of Electronics and Communications Engineering, University Centre for Research and Development, Chandigarh University, 140413, Mohali, Punjab, India
5 Centre for Nonlinear Systems, Chennai Institute of Technology, 600069, Chennai, India
Accepted: 30 July 2023
Published online: 4 August 2023
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.
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