Superstability and optimal multiparameter suppression of chaotic dynamics for a class of autonomous systems with quadratic nonlinearities (Q414066)

The authors consider a system formed by three ordinary differential equations whose right hand sides are defined by polynomials of degree two. It is assumed that the system exhibits a chaotic behavior. The aim is to stabilize all the equilibrium points of the system by means of local corrections (possibly dependent on the point) of the entries of the Jacobian matrix of the system. In such a way, the chaotic behavior is avoided. For this property, a necessary and sufficient condition is stated. Then, assuming that the problem is solvable, the authors show how to obtain optimal corrections (in the sense of the minimal norm).