Almost Periodic Solutions of Recurrently Structured Impulsive Neural Networks - Akhmet, Marat; Erim, Gulbahar (Discontinuity, Nonlinearity, and Complexity, 2026)
The model under discussion is an elaborated recurrent impulsive neural network. This is the first time in literature that the impacts are structured completely as the original neural network, such that physical sense of impacts has been explained. Moreover, the impact part comprises all types of impacts in neural networks, which were traditionally studied in conservative models. In the research, neuron membranes with negative as well as positive capacitance, are considered newly as parts of the neural networks. This was not studied before. The system is analyzed in matrix form to facilitate more transparent presentation. The existence and uniqueness of asymptotically stable discontinuous almost periodic solutions are investigated. An example with simulations is provided to illustrate the results.