Conditions of the existence of an attractor in the form of a quadric for polynomial systems
The author studies a polynomial dynamical system \[ dx_i/dt= f_i(x)=-a_{i0}- \sum^n_{j=1} a_{ij}x_j -\sum^n_{j,k=1} a_{ijk} x_jx_k- \sum^n_{j,k,l=1} a_{jkl} x_jx_kx_l, \] and derives conditions for the existence of an attractor in the form of a quadric. According to the author, the study is meant to develop methods of synthesis and optimization of self-oscillation and other multiregime dynamical systems.
scientific article; zbMATH DE number 1050497