arXiv subjects
Publications and source records attributed to E. P. Volokitin.
We study plane quadratic and cubic differential systems satisfying the Caushy - Riemann conditions. We construct all global topologically equivalent phase portraits of the systems.
We construct a global bifurcation diagram of the plane differential system $$ {l} \dot x = x(1-x)-x y/(a+x^2), \dot y = y(δ-βy/x), x(t)>0, y(t)>0, a>0, δ>0, β>0, $$ which describes the predator-prey interaction.
We study a specific family of uniformly isochronous polynomial systems. Our results permit to solve a problem about centers of such systems.
We study a connection between the isochronicity of a center of a polynomial vector field and the existence of a polynomial commuting system. We demonstrate an isochronous system of degree 4 which does not commute with any polynomial system. We prove that among the Newton polynomial systems only the Lienard and Abel systems may commute with transversal polynomial fields. We give a full and constructive description of centralizers of the Abel polynomial systems. We give new examples of isochronous systems.