Neural mass models (NMM) seek to unveil the fundamental principles governing macroscopic neural activity, drawing insights from the brain's intricate and multi-scale structure. The advent of an exact mean-field theory for networks of quadratic integrate-and-fire (QIF) neurons represents a significant leap forward in our comprehension of the link between microscale neural mechanisms and mesoscopic brain activity [1]. This model establishes a robust coupling between two biophysically relevant macroscopic quantities: the firing rate and the mean membrane potential, which collectively drive the evolution of the neuronal network. In this study, we analyze a next-generation pyramidal-interneuron (PING) neural mass model employing the exact mean-field theory for QIF neurons. Prior research has underscored the capacity of this type of NMM variant to furnish a more precise and nuanced understanding of synaptic dynamics [2,3]. Our study begins with an extensive bifurcation analysis of the model's parameter space, aimed at better understanding its inherent properties and identifying both periodic and chaotic dynamics. Furthermore, we study the response of neural populations to periodic stimulation, inspired by therapies such as transcranial Alternating Current Stimulation (tACS). In this part, we investigate the entrainment of the neural populations and how it impacts the average firing rates and their frequencies, also calculating different local field potential (LFP) proxies [4]. Our findings provide insights into brain function and might serve as a guide for devising more effective brain stimulation techniques.