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

• Published in: Nonlinear dynamics Vol. 107; no. 3; pp. 2867 - 2886
• Main Authors: Njitacke, Zeric Tabekoueng, Awrejcewicz, Jan, Ramakrishnan, Balamurali, Rajagopal, Karthikeyan, Kengne, Jacques
• Format: Journal Article
• Language: English
• 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
• DOI: 10.1007/s11071-021-07109-4
• ISSN: 0924-090X

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.