https://doi.org/10.1140/epjp/s13360-024-05363-0
Regular Article
Dynamical properties of a small heterogeneous chain network of neurons in discrete time
1
School of Mathematical and Computational Sciences, Massey University, Colombo Road, 4410, Palmerston North, New Zealand
2
School of Digital Sciences, Digital University Kerala, Technopark Phase-IV Campus, Mangalapuram, 695317, Kerala, India
3
EpiCentre, School of Veterinary Science, Massey University, 4410, Palmerston North, New Zealand
4
Department of Mathematical Sciences, Auckland University of Technology, 1010, Auckland, New Zealand
Received:
25
March
2024
Accepted:
13
June
2024
Published online:
24
June
2024
We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark–Sacker, double Neimark–Sacker, flip- and fold-Neimark–Sacker, and 1 : 1 and 1 : 2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.
© The Author(s) 2024
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