The chapter presents theoretical and numerical findings on recurrent oscillations in Cohen-Grossberg neural networks. The investigation focuses on the model with variable inputs and strengths of connectivity, which are alpha unpredictable or Poisson stable functions. A method of reducing a nonlinear model into quasi-linear systems using an integral transformation is presented. This approach helps analyze complex nonlinear systems, making applying a well-proven linear approximation method possible. A particular case, when the coefficients are compartmental with periodic and alpha unpredictable ingredients, is also carefully researched. Sufficient conditions are obtained to guarantee the existence of exponentially stable alpha unpredictable outputs of the models. They are specified for Poisson stability by utilizing the unique method of included intervals. By numerical and graphical analysis, it is shown how a constructive technical characteristic, the degree of periodicity, reflects the contributions of the ingredients in the final outputs of the neural networks.