Bifurcation with memory

Journal Article · Mon Mar 31 23:00:00 EST 1986 · SIAM J. Appl. Math.; (United States)

DOI:https://doi.org/10.1137/0146013· OSTI ID:5739302

Olmstead, W E; Davis, S H; Rosenblat, S; Kath, W L

A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda, controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda = lambda/sub 1/, separating purely steady (lambda < lambda/sub 1/) from combined steady/T-periodic (lambda > lambda/sub 1/) states with T ..-->.. infinity as lambda ..-->.. lambda/sup +//sub 1/. Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda = lambda/sub 1/.

• Research Organization: Dept. of Engineering Sciences and Applied Mathematics, Northwestern Univ., Evanston, IL 60201
• DOE Contract Number: AC02-78ER04650
• OSTI ID: 5739302
• Journal Information: SIAM J. Appl. Math.; (United States), Journal Name: SIAM J. Appl. Math.; (United States) Vol. 46:2; ISSN SMJMA
• Country of Publication: United States
• Language: English

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