Nonlinear Phenomena in Complex Systems, 2001, Vol.4, No.4, pp.376-382

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2001, Volume 4, Number 4, pp.376-382

Complex Dynamics of Simple Models of Distributed Self--Oscillating Delayed Feedback Systems
T.V.Dmitrieva, N.M.Ryskin, and A.M.Shigaev

Spatio-temporal chaos in several distributed delayed feedback systems are studied. In the first part of the work simple models described by differential equations with a delayed term are considered. Among them are the model of a delayed feedback oscillator with cubic nonlinearity and that of a microwave klystron oscillator. Then the models of distributed parametric oscillators based on a parametric coupling of waves nonlinear medium are studied. The mechanisms of self-modulation and scenarios of transition to chaos in all considered systems are investigated in details. Presented results help to find the common features specific for distributed systems with delayed feedback and to take an advantage in understanding of peculiarities of nonlinear dynamics of systems with many degrees of freedom
Key words: spatio-temporal chaos, delayed feedback oscillator, klystron, distributed parametric oscillator, parametric instability

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