ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34 Yanchuk, Sergiy, Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine Conditions for existing of cycles in some two-dimensional system of differential equations We consider two-dimensional system of ordinary differential equations

\frac{dx}{dt} = α[y − δx + f(x)], \frac{dy}{dt} = x − y + z,

with piece-wise linear right side f(x) = x − \frac{1}{2} (|x + 1| − |x − 1|). This system describes the behavior of Chua’s electronic circuit under appropriate conditions on it’s elements. The coefficient criteria for existing of cycles will be presented.