Investigation of convergence of large scale almost periodic systems by means of comparison vector functions with components as forms of even degrees

Abstract

By V. M. Matrosov's comparison method we obtain sufficient conditions of convergence for a large scale almost periodic system of differential equations. As components of comparison vector functions we use the homogeneous forms of even degrees. We propose a new approach to construction of comparison system that leads to the best results with respect to known F.

On convergence conditions for generalized Persidskii systems

“…We may additionally ask for preservation conditions for the attracting solution of the (almost) periodicity of the input 12,13 . Note that in nonlinear systems, the frequency of entertainment is not necessarily kept by the output 14 , and a typical example is again the Duffing's model, which can generate chaotic trajectories under harmonic excitation.…”

“…We may additionally ask for preservation conditions for the attracting solution of the (almost) periodicity of the input. 12,13 Note that in nonlinear systems, the frequency of entertainment is not necessarily kept by the output, 14 and a typical example is again the Duffing's model, which can generate chaotic trajectories under harmonic excitation. The relations between the existence of almost periodic solutions and properties of the right-hand sides of dynamical systems were intensively studied during the last century (see, e.g., Markov's theorem 15 ).…”

Convergence conditions for Persidskii systems

“…We may additionally ask for conditions of preservation by the attracting solution of the (almost) periodicity of the input [12], [13]. Note that in nonlinear systems, the frequency of entrainment is not necessarily kept by the output [14], and a typical example is again Duffing's model, which can generate chaotic trajectories under harmonic excitation.…”