Homoclinic Orbits in 3D Dissipative Systems

 

Anatoly Andreevich Martynyuk

Nelli Vladimirovna Nikitina

 

The paper deals with a variational system corresponding to a three-dimensional dynamic system. The characteristic equation of the variational system depends on partial solutions. The matrix of the right-hand part of the variational system is a sum of two matrices. One matrix contains the spectrum of the linear system and the other one represents partial solutions. Two theorems, determining the sign of the sum of the characteristic exponents of a point on a homoclinic trajectory, are proved.

Key words: dynamic system, dissipative system, variational systems, homoclinic orbit.