The chapter delves into the dynamics of shunting inhibitory cellular neural networks encompassing continuous and discontinuous behaviors. The initial focus is on a model featuring compartmental periodic alpha unpredictable coefficients and input data. An algorithm that expands the alpha unpredictable functions by applying diagonalization to the arguments of functions of several variables is proposed. Sufficient conditions for the existence and uniqueness of exponentially stable alpha unpredictable and Poisson stable outputs are established using the method of included intervals and verifying the separation property. Furthermore, a model with continuous time-varying rates and inputs, incorporating compartmental passive decay rates characterized by periodic and Poisson stable components, is investigated. The periodic component ensures Poisson stability, while another induces irregular oscillations. The synchronization of convergence sequences for the rates and inputs yields the required outputs. The exploration extends to shunting inhibitory cellular neural networks with impulses, a piecewise constant argument, and symmetry between the impulsive and differential components of the models. The symmetry enhances understanding of network dynamics and modeling capabilities. Simulation examples are provided to elucidate theoretical findings, demonstrating the robustness and practical applicability of the proposed models across diverse scenarios.