Nonlinear Phenomena in Complex Systems, 2019, Vol.22, No.2, pp.190

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2019, Vol.22, No.2, pp.190 - 195

Non-rough Relaxation Solutions of a System with Delay and Sign-Changing Nonlinearity
Alexandra Kashchenko

In this paper we study nonlocal dynamics of a system of two coupled delay differential equations with a sign-changing compactly supported nonlinearity. The main assumptions in the problem are that nonlinearity is multiplied by a large parameter and a coupling coefficient is sufficiently small. Using asymptotic methods we investigate the existence of relaxation periodic solutions of a given system. We choose a special set in the phase space of the initial system. Then we calculate asymptotics of all solutions of the considered system with initial conditions from a chosen set. By this asymptotics we build a special mapping. Cycles of this mapping correspond to periodic asymptotic (by the discrepancy) solutions of the initial system. Constructed mapping has a two-parameter families of non-rough cycles. Thus, the initial system has two-parameter families of non-rough inhomogeneous relaxation periodic asymptotic (by the discrepancy) solutions.

Key words: asymptotics, nonlocal dynamics, delay, large parameter, relaxation oscillation

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