Our main goal in this project is to perturbation Kolmogorov Systems on planar piecewise vector fields defined in two zones separated by a straight line and study how many limit cycles can be obtained.In addition, we intend to approach the Kolmogorov Systems through Sotomayor-Teixeira regularization. It is well known that different regularizations can lead to different ways of defining sliding solutions on. In addition, from a theoretical point of view, assuming only linear regularization would neglect a vast expanse of phenomena occurring in smooth systems approaching pointwisely to non-smooth ones. Therefore, our main goal at this point is to consider two Kolmogorov Systems and study the regularization when both $\varphi$ is a monotonic function and $\varphi$ is not a monotonic function.
News published in Agência FAPESP Newsletter about the scholarship: