In the chapter, we explore the presence of alpha unpredictable recurrence within various models of Hopfield-type neural networks, given as differential equations outlined in Preliminaries. The start model is with modulo-periodic alpha unpredictable synaptic connections, rates, and external inputs. They synchronize to ensure the output convergence on compact subsets of the real axis as Poisson stability requires. Subsequently, impulsive neural network models are presented: one with fixed coefficients and another with variable ones. The latter allows for dynamic changes in convergence properties and stability as coefficients adjust, making it suitable for tasks where underlying relationships or patterns evolve. Both have a symmetrical nature, which facilitates a detailed examination of network states during sharp jumps, enabling the exploration of complex models of processes with impulses and the satisfaction of the original ideas of J. Hopfield. Finally, the chapter extends the method for studying alpha unpredictable oscillations to neural networks with piecewise constant arguments. The theoretical foundation of the analysis relies on the method of included intervals, which is extended to B-topological spaces of discontinuous functions. All theoretical findings are substantiated through numerical examples and simulations, underpinning the robustness and applicability of the proposed models and analytical techniques.