A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “A modification of Hutchinson's equation”, Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 12,Pages <nobr>2099

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A modification of Hutchinson's equation

A. Yu. Kolesov^a, E. F. Mishchenko^b, N. Kh. Rozov^c

^a Faculty of Mathematics, Yaroslavl State University, Sovetskaya ul. 14, Yaroslavl, 150000 Russia
^b Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333 Russia
^c Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia

Abstract: A new mathematical object is introduced, namely, a scalar nonlinear delay differential-difference equation is considered that is a modification of Hutchinson's equation, which is well known in ecology. The existence and stability of its relaxation self-oscillations are analyzed.

Key words: differential-difference equation, relaxation cycle, asymptotic behavior, stability.

UDC: 519. 624.2

Received: 26.04.2010