The periodic solutions of a class of cubic delay differential system (Q1916509)

A polynomial differential system (1) \(x'(t) = P(x(t), x(t - s), y(t), y(t - s))\), \(x'(t) = R(x(t), x(t - s), y(t), y(t - s))\), in which \(P(x,x,y,y) = - y (\mu + bx^2 + cy^2)\), \(\lambda > 0\), \(\mu > 0\), \(R(x,x,y,y) = x (\lambda + ax^2 + by^2)\), \(ac > 0\), \(s > 0\), is considered. Under some sign conditions on \(a,b,c\) a theorem on existence of an infinite number of nonconstant periodic solutions to (1) is demonstrated.