ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kashchenko S. A., Kashchenko I. S. Asymptotics of complex spatio-temporal structures in the systems with large delay. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 4, pp. 137-146. DOI: 10.18500/0869-6632-2008-16-4-137-146

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Asymptotics of complex spatio-temporal structures in the systems with large delay

Kashchenko Sergej Aleksandrovich, P. G. Demidov Yaroslavl State University
Kashchenko I. S., P. G. Demidov Yaroslavl State University

The local dynamics is considered of differential equations with two delays in the case of one delay is asymptotically large. Under this condition, critical cases have infinite dimension. As the normal form equations the Ginzburg–Landau equations have been. Their nonlocal dynamics defines local behavior of solutions of initial equations. 

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  1. Landa PS. Self-Oscillations in Distributed Systems. Moscow: Nauka; 1983. 320 p. (in Russian).
  2. Dmitriev AS, Kislov VY. Stochastic Oscillations in Radiophysics and Electronics. Moscow: Nauka; 1989. 280 p. (in Russian).
  3. Kuznetsov, SP. Complex dynamics of oscillators with delayed feedback (review). Radiophys. Quantum Electron. 1982;25(12):996–1009. DOI: 10.1007/BF01037379.
  4. Kilias T, Kutzer K, Moegel A, Schwarz W. Electronic chaos generators – design and applications. International Journal of Electronics. 1995;79(6):737–753. DOI: 10.1080/00207219508926308.
  5. Maistrenko YL, Romanenko EN, Sharkovsky AN. Difference Equations and Their Applications. Dordrecht: Springer; 1993. 358 p. DOI: 10.1007/978-94-011-1763-0.
  6. Kashchenko SA. Bifurcation peculiarities of a singularly perturbed equation with delay. Siberian Mathematical Journal. 1999;40(3):567–572 (in Russian).
  7. Kashchenko SA. Application of the normalization method to the study of the dynamics of differential-difference equations with a small factor at the derivative. Differential Equations. 1989;25(8):1448–1451 (in Russian).
  8. Kashchenko IS. Dynamic properties of first-order equations with large delay. Modeling and Analysis of Information Systems. 2007;14(2):58–62 (in Russian).
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