Circuit implementation of the mathematical model of neurons represents an alternative approach for the validation of their dynamical behaviors for their potential applications in neuromorphic engineering. In this work, an improved FitzHugh–Rinzel neuron, in which the traditional cubic nonlinearity is swapped with a sine hyperbolic function, is introduced. This model has the advantage that it is multiplier-less since the nonlinear component is just implemented with two diodes in anti-parallel. The stability of the proposed model revealed that it has both stable and unstable nodes around its fixed points. Based on the Helmholtz theorem, a Hamilton function that enables the estimation of the energy released during the various modes of electrical activity is derived. Furthermore, numerical computation of the dynamic behavior of the model revealed that it was able to experience coherent and incoherent states involving both bursting and spiking. In addition, the simultaneous appearance of two different types of electric activity for the same neuron parameters is also recorded by just varying the initial states of the proposed model. Finally, the obtained results are validated using the designed electronic neural circuit, which has been analyzed in the Pspice simulation environment.
This paper recounts the dynamical investigations and microcontroller validation of Josephson junction (JJ) driven by Wien bridge circuit (WBC). Relying on the stability analysis of two equilibrium points found in JJ driven by WBC (JJDWBC), it is revealed that one equilibrium point is unconditionally stable while the other equilibrium point is unstable. The JJDWBC exhibits reverse period-doubling bifurcation, periodic attractors, period-doubling bifurcation, bistable chaotic attractors, and different presentations of monostable chaotic attractors. Partial and total amplitude controls are achieved by adding two controller parameters into the rate equations of JJDWBC. Finally, the microcontroller implementation is used to validate the dynamical behaviors found in JJDWBC.
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