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A Phase Control Method for the Dynamical Attractor of the HR Neuron Model: The Rotation-Transition Process and Its Experimental Realization

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Abstract

Since the definitions of the biological neuron model are similar to the oscillator structures, many control theorems are used in common with the biological neuron model. While the stability and the synchronization etc. control methods are frequently studied subject for these nonlinear systems, the “rotation-transition” concept draws attention in the recent studies dealing with nonlinear dynamical systems. The studies about the rotation-transition of the nonlinear systems are usually focused on the chaotic oscillator structures. On the other hand, the concept of the rotated attractor is also encountered in the dynamics of biological systems and there is no research about the rotation-transition of biological neuron models. In this study, the rotation-transition process of the Hindmarsh–Rose neuron model has been performed for the first time. In this context, firstly, the HR neuron model is converted to a rotated structure by using the Euler’s rotation theorem. Then, the characteristics outcomes of the rotated HR neuron model are analyzed by calculating the equilibrium points and Lyapunov exponents. The functionality of the rotated HR neuron model has been tested by the numerical simulation studies. Lastly, the rotated HR neuron model is implemented by using FPGA device. Briefly, this conversion process is modeled mathematically, then supported by the results of numerical simulations and finally verified by the results of the FPGA based experimental realizations. Thus, a phase control method for the dynamical attractor of a neuron model is achieved without the need for any coupling identification in this system.

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  1. Department of Electrical and Electronics Engineering, Kayseri University, 38280, Kayseri, Turkey

    Nimet Korkmaz

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Correspondence to Nimet Korkmaz.

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Korkmaz, N. A Phase Control Method for the Dynamical Attractor of the HR Neuron Model: The Rotation-Transition Process and Its Experimental Realization. Neural Process Lett 53, 3877–3892 (2021). https://doi.org/10.1007/s11063-021-10568-w

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