Almost periodic solutions of recurrently structured impulsive neural networks

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2022-3-28
Top, Gülbahar
This thesis aims to conduct detailed and precise neural networks research with impulses at nonprescribed moments in terms of periodic and almost periodic solutions. Most of the actions in nature modeled by neural networks involve repetitions. Hence periodic and almost periodic motions become crucial. So in this thesis, the existence, uniqueness, and stability of the periodic and almost periodic motion are served for the neural networks with prescribed and nonprescribed impacts. This impulsive system is a neural network with innovative structured impacts that perfectly match the rates. If one regards the impulses as limits of their continuous counterparts, this makes sense for the application. Thus, the novel system also considers the neural networks' nature in the impulsive part since the sudden noises or impact disturbances can affect the rates or activation functions. New conditions on the coefficients have been designed to be more specific and detailed. The constructive stability conditions are delivered directly related to the system's coefficients. A detailed approach is performed to the systems with variable moments of impulses. For the research, the method of B-equivalence is employed, and the relationship between the original and B-equivalent systems was explicitly established and provided. Furthermore, because the impulsive component of the system is inherent to the neural network, the B-equivalent system also matches the original structure in terms of differential and impulsive parts. One of the novel aspects of this work is that the possibility of negative capacitance in a neurological system is not neglected. Together with the elimination of the capacitance's positivity requirement, the new structure allows for a more thorough study under optimal conditions. The probability of negative capacitance emphasizes the need for impulses to maintain stability.

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Citation Formats
G. Top, “Almost periodic solutions of recurrently structured impulsive neural networks,” Ph.D. - Doctoral Program, Middle East Technical University, 2022.