Estimations of the Domains of Attraction for Classes of Nonlinear Continuous Polynomial Systems

The present study tackles the problem of assessing asymptotically stable regions for nonlinear, continuous, analytic, and autonomous systems of a particular category. The second section provides a polynomial explanation of each system under study using the Kronecker tensorial product and the generalised Taylor-series expansions. The third section is reserved for determinations of regions of assured stability. The last section provides a derivation of algebraic methods for enlarging initially stable regions that are assured to be exponentially stable. Numerical instances are described to demonstrate the validity of the method evolved for the well-known Hahn and Van der Pol modelling equations.