RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Model. Anal. Inform. Sist.: Year: Volume: Issue: Page: Find

 Model. Anal. Inform. Sist., 2013, Volume 20, Number 3, Pages 43–57 (Mi mais310)

Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell Domain

S. D. Glyzin, P. L. Shokin

P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia

Abstract: We consider a boundary problem of reaction-diffusion type in the domain consisting of two rectangular areas connected by a bridge. The bridge width is a bifurcation parameter of the problem and is changed in such way that the measure of the domain is preserved. The conditions on chaotic oscillations emergence were studied and the dependence of invariant characteristics of the attractor on the bridge width was constructed. The diffusion parameter was chosen such that in the case of widest possible bridge (corresponding to a rectangular domain) the spatially homogeneous cycle of the problem is orbitally asymptotically stable. By decreasing the bridge width the homogeneous cycle looses stability and then the spatially inhomogeneous chaotic attractor emerges. For the obtained attractor we compute Lyapunov exponents and Lyapunov dimension and notice that the dimension grows as the parameter decreases but is bounded. We show that the dimension growth is connected with the growing complexity of stable solutions distribution with respect to the space variable.

Keywords: diffusion chaos, attractor, Lyapunov dimension, Ginzburg–Landau equation, bifurcation.

Full text: PDF file (1439 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 517.9

Citation: S. D. Glyzin, P. L. Shokin, “Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell Domain”, Model. Anal. Inform. Sist., 20:3 (2013), 43–57

Citation in format AMSBIB
\Bibitem{GlySho13} \by S.~D.~Glyzin, P.~L.~Shokin \paper Diffusion Chaos in Reaction -- Diffusion Boundary Problem in the Dumbbell Domain \jour Model. Anal. Inform. Sist. \yr 2013 \vol 20 \issue 3 \pages 43--57 \mathnet{http://mi.mathnet.ru/mais310}