Conditions for the existence of limit cycles of the second kind for a system of differential equations: I (Q610333)

The paper deals with the following system of differential equations \[ \dot{x}=Ax+b\varphi(\sigma), \quad \dot{\sigma}=c^{T}x+\varrho \varphi(\sigma), \] where \(A\) is an \(n \times n\) matrix, \(x, c, b\in \mathbb R^n\), \(\varrho \leq 0\), \(\varphi(\sigma)\) is a \(\Delta\)-periodic continuously differentiable function. This system is a mathematical model for phase synchronization. By using a nonlocal reduction method, the author obtains conditions for the existence of several limit cycles of the second kind.