Hamiltonian energy computation and complex behavior of a small heterogeneous network of three neurons: circuit implementation

Brain functions are sometimes emulated using some analog integrated circuits based on the organizational principle of natural neural networks. Neuromorphic engineering is the research branch devoted to the study and realization of such circuits with striking features. In this contribution, a novel s...

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Published inNonlinear dynamics Vol. 107; no. 3; pp. 2867 - 2886
Main Authors Njitacke, Zeric Tabekoueng, Awrejcewicz, Jan, Ramakrishnan, Balamurali, Rajagopal, Karthikeyan, Kengne, Jacques
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.02.2022
Springer Nature B.V
Subjects
Analog circuits
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Integrated circuits
Liapunov exponents
Mathematical models
Mechanical Engineering
Neural networks
Neurons
Nonlinear analysis
Original Paper
Parameters
Two dimensional models
Vibration
Hamilton energy
FitzHugh–Nagumo neuron
Multistability
Hindmarsh–Rose neurons
Circuit implementation
Network of three neurons
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Summary:Brain functions are sometimes emulated using some analog integrated circuits based on the organizational principle of natural neural networks. Neuromorphic engineering is the research branch devoted to the study and realization of such circuits with striking features. In this contribution, a novel small network of three neurons is introduced and investigated. The model is built from the coupling between two 2D Hindmarsh–Rose neurons through a 2D FitzHugh–Nagumo neuron. Thus, a heterogeneous coupled network is obtained. The biophysical energy released by the network during each electrical activity is evaluated. In addition, nonlinear analysis tools such as two-parameter Lyapunov exponent, bifurcation diagrams, the graph of the largest Lyapunov exponent, phase portraits, time series, as well as the basin of attractions are used to numerically investigate the network. It is found that the model can experience hysteresis justified by the simultaneous existence of three distinct electrical activities using the same set of parameters. Finally, the circuit implementation of the network is addressed in PSPICE to further support the obtained results.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-021-07109-4