Both positive and negative feedback mechanisms are vital in a number of biologically relevant processes. For example, feedback loops are essential for limb development in mammals and are responsible for constraining growth in plants to the specific regions. Controlling feedback mechanisms within the fully synthetic materials is important for a range of biomimetic functionalities. Herein, using three-dimensional Gel Lattice Spring Model-based simulations, we focus on the two types of hydrogels, pure Poly(N-isopropylacrylamide) (PNIPAAm) hydrogels and PNIPAAm gels functionalized with light-sensitive trisodium salt of copper chlorophyllin. Prior experimental studies had shown that illumination of the latter gels results in their heating and in discontinuous volume phase transitions; the results of our simulations are in a good agreement with these experimental studies. We consider thin hydrogel membranes under different confinements and under the influence of such external stimuli as temperature gradients and light. We focus on pattern development during the volume phase transitions as the samples re-swell under the confinement. Our results demonstrate that these gels exhibit rich steady-state bucking patterns (including well-ordered patterns) for the chosen gel parameters and confinement conditions. We show that one can effectively utilize external stimuli (light or temperature gradients) to control specific pattern selection and well as feedback mechanisms in these systems.