The Introduction comprises three large compartments: a brief overview of neural networks, a presentation of hybrid differential equations, and a description of the main dynamical actors of the play, alpha unpredictability, ultra Poincaré chaos, and alpha unpredictable functions. After the short description of a biological neuron and artificial neural networks, a historical and structural outline of models focused on the research is made. The neural network presentations start with S. Haykin’s definition and are finalized in detail of Hopfield, Cohen-Grossberg, shunting inhibitory cellular and inertial neural networks. A short outline of the modeling investigation is presented. Impulsive systems and differential equations with piece-wise constant argument are considered as hybrid systems, which combine various sorts of discontinuity with continuous rate. The first glance at the necessity of the models for neuroscience is made. Throughout the book, the significance of discontinuous models will be emphasized several times. Besides regular recurrence, an alpha unpredictable motion was recently created to join what is known as chaos, if having a classical dynamical systems background, focused on individual motions. The information on the symbiosis is provided in the last part of the chapter.