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Abstract

The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one- and/or two-spatial dimensions.
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Authors and Affiliations

Adel Ouannas
1
Fatiha Mesdoui
2
Shaher Momani
2 3
Iqbal Batiha
4 3
Giuseppe Grassi
5

  1. Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
  2. Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
  3. Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
  4. Department of Mathematics, Faculty of Science and Technology, Irbid National University, 2600 Irbid, Jordan
  5. Dipartimento Ingegneria Innovazione, Universitadel Salento, 73100 Lecce, Italy

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