Total Poisson Boundedness of Solutions of $${\cal P}$$-Perturbed Complex Systems of Differential Equations

Abstract

We introduce the concepts of $${\cal P}$$-perturbed system and, in particular, $${\cal P}$$-perturbed complex system. Based on the method of Lyapunov functions, we obtain the sufficient condition of total Poisson boundedness of solutions to the $${\cal P}$$-perturbed system with respect to any linear system with constant coefficients. Based on the method of vector Lyapunov functions and the above-stated condition, we obtain sufficient conditions of total Poisson boundedness of solutions to the $${\cal P}$$-perturbed complex system and solutions to the $${\cal P}$$-perturbed complex system with feedback loop.