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The investigation in this paper is founded on the theoretical study of a neuronal circuit driven by a Josephson junction (JJ) under the effects of light and temperature, and its microcontroller design. The neuronal circuit is made of a resistor in series to a phototube (PT) to which an excitation which is a direct current (DC) source, a thermistor, and a capacitor is linked to this formalism via the parallel connection. The system describing the neuronal circuit has 2 or no equilibrium points with a direct consequence on the excitation current and constant voltage of PT. Stability explorations reveal a stable node or focus and a saddle-node for the reported two equilibrium points. The hysteresis loops' appearances are dependent on the temperature, damping parameter, and constant voltage across the PT. Continuous spiking oscillations, periodic and periodic bursting oscillations, chaotic and coexisting attractors as a function of the temperature, and modulation parameters of a sinusoidal voltage of PT are characterized via numerical simulations. Quantitatively, the theoretical results are similar to the experimental results achieved via the microcontroller implementation of the model of the neuronal circuit founded on the JJ under the effects of light and temperature.

Artificial neural networks are generally used to emulate some biological activities of the brain. Those neurons in the network are connected to others through synapses. As a result, several works have been devoted to the design of various artificial synapses, including the Josephson Junction Synapse (JJS). In this contribution, a model of the Hindmarsh–Rose neuron coupled with a FitzHugh–Nagumo neuron through a JJS is considered. That JJS enables us to simulate the effects of the magnetic field by providing additional phase error between the junctions. The Hamilton function related to the energy released by the coupled neurons during the transition between electrical activities is determined using the Helmholtz theorem. The equilibrium points of the proposed model are investigated, and their stability justifies the self-excited dynamics of the model. During studies, sets of phenomena such as Hopf bifurcation, double Hopf bifurcation, periodic spikings, periodic and chaotic burstings, (resp. firings) are found. More importantly, several coexisting activities are found in the coupled neurons as well as hyperchaotic firing activities rarely reported in such classes of neurons. Finally, PSpice simulations are used to further support results obtained from the mathematical model of coupled neurons through a JJS. • Coupled heterogeneous neurons. • Hamilton energy computation. • Josephson junction synapse. • Extremely rich dynamics. • Circuit implementation. [ABSTRACT FROM AUTHOR]

• We report the dynamics of heterogeneous coupled neurons made of mHR and FN models. • We demonstrate that the coupled neurons have a Hamilton energy that enables, to keep the electrical activity of the model. • The numerical simulations reported a window of the electromagnetic induction strength where the model exhibits hysteretic dynamics. • The STM32F407ZE microcontroller development board is exploited for digital implementation of the proposed coupled model. • Compressive sensing approach is jointly used with chaotic sequences to compress and encrypt digital images based on the DWT. This paper studies the effect of the electromagnetic flux on the dynamics of an introduced model of heterogeneous coupled neurons. Analytical investigation of the coupled neurons revealed that the obtained model is equilibrium free thus displays hidden firing activities. Based on the Helmholtz theorem, it is demonstrated that the coupled neurons possess a Hamilton energy, which enables to keep the electrical activity of the coupled neurons. Numerical simulations based on the fourth-order Runge-Kutta formula have enabled us to find a range of the electromagnetic induction strength where the model exhibits hysteretic dynamics. That hysteresis justifies the coexistence of two different firing activities for the same parameters captured. This latter behavior is further supported using bifurcation diagrams, the graph of the maximum Lyapunov exponent, phase portraits, time series, and attraction basins as arguments. Beside, the STM32F407ZE microcontroller development board is exploited for the digital implementation of the proposed model. The results of microcontroller implementation perfectly supported the results of the numerical simulation of bistability. Finally, a compressive sensing approach is used to compress and encrypt digital images based on the sequences of the above coupled-neurons model. The plain color image is decomposed into R, G, and B components. The DWT is applied to each component to obtain the corresponding sparse components. Confusion keys are obtained from the proposed coupled neurons to scramble each sparse component. The measurement matrixes obtained from the coupled neurons sequence are used to compress the confused sparse matrices corresponding to R, G, and B components. Each component is quantified, and a diffusion step is then applied to improve the randomness and consequently the information entropy. [ABSTRACT FROM AUTHOR]