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 equals lambda //1, separating purely steady ( lambda less than lambda //1) from combined steady/T-periodic ( lambda less than lambda //1) states with T yields infinity as lambda yields lambda //1** plus . 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 equals lambda //1.
ASJC Scopus subject areas
- Applied Mathematics