Abstract
We consider a differential-difference equation of second order of delay type, containing the delay of the function and its derivatives. Such equations occur in the modeling of electronic devices. The nature of the loss of the zero solution stability is studied. The possibility of stability loss related to the passing of two pairs of purely imaginary roots, that are in resonance 1:3, through an imaginary axis is shown. In this case bifurcating oscillatory solutions are studied. It is noted the existence of a chaotic attractor for which Lyapunov exponents and Lyapunov dimension are calculated. As an investigation techniques we use the theory of integral manifolds and normal forms method for nonlinear differential equations.
Highlights
Изучается характер потери устойчивости нулевого решения уравнения (1) и бифуркации автоколебательных решений в критическом случае потери устойчивости
В результате получим систему алгебраических уравнений
И изучим расположение корней ее характеристического уравнения
Summary
Изучается характер потери устойчивости нулевого решения уравнения (1) и бифуркации автоколебательных решений в критическом случае потери устойчивости. И изучим расположение корней ее характеристического уравнения Для этого воспользуемся методом D-разбиений [1], который позволяет исследовать движение корней уравнения (3) при изменении параметров и построить в пространстве параметров области устойчивости и неустойчивости решени√й уравнения (1).
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