Complex dynamics from heterogeneous coupling and electromagnetic effect on two neurons: Application in images encryption

• Published in: Chaos, solitons and fractals Vol. 153; p. 111577
• Main Authors: Tabekoueng Njitacke, Zeric, Tsafack, Nestor, Ramakrishnan, Balamurali, Rajagopal, Kartikeyan, Kengne, Jacques, Awrejcewicz, Jan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2021
• Subjects: Coexistence of hidden firing patterns; Compressive sensing; FitzHugh-Nagumo(FN) neuron; Hamilton energy; Image encryption; Memristive Hindmarsh-Rose(mHR) neuron; Microcontroller implementation; Image encryption; Compressive sensing; Coexistence of hidden firing patterns; Microcontroller implementation; Hamilton energy; FitzHugh-Nagumo(FN) neuron; Memristive Hindmarsh-Rose(mHR) neuron
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2021.111577

•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.