Complexity and synchronization in models are necessary for research in neuroscience. In our talk the complexity will be present through special type of bifurcations - the medusas bifurcations in the Cowan-Wilson model, they have been introduced in our recent papers. Synchronization of biological integrate-and-fire oscillators will be discussed considering the C. Peskin model. The collective behavior of biological and chemical oscillators is a fascinating topic that has attracted a lot of attention in the last 50 years. The integrate-and-fire model of the cardiac pacemaker was developed by C.Peskin to a population of identical pulse-coupled oscillators. The model has been widely adapted for neuroscience. In the present research we give a solution of the second conjecture of Peskin. The talk will consists of main results, simulations and discussion of possible extensions. We will discuss what kind of benefits can be obtained from the study for the artificially intelligent systems, robotics and electronics.