BERNULLI DIFFERENTIAL EQUATION AND CHAOS

Abstract

Existence conditions of homoclinic orbits for some systems of ordinary quadratic dif­ferential equations with singular linear part are founded. A realization of these conditions guarantees the existence of chaotic attractors at 3-D autonomous quadratic systems. In addition, a chaotic behavior of the solutions of these systems is determined by one-dimensional discrete map at some values of parameters. Examples are given.

Keywords

• гомоклинические орбиты
• сингулярная линейная часть
• хаотические атракторы