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Volume 20,     Number 1,     Spring 2012

 

GLOBAL HOPF BRANCHES IN A DELAYED
MODEL FOR IMMUNE RESPONSE TO HTLV-1
INFECTIONS: COEXISTENCE OF MULTIPLE
LIMIT CYCLES
MICHAEL Y. LI, XIHUI LIN AND HAO WANG

Abstract. For an HTLV-I infection model, Li and Shu has shown in [6] that delayed CTL response can lead to complex bifurcations, and in particular, coexistence of multiple stable periodic solutions. In this paper, we extend results of Li and Shu in [6] and investigate the case when there exist three sequences of Hopf bifurcation points. Through numerical simulations, we show that two of the sequences lead to bounded global Hopf bifurcation branches as observed in [6], and a third sequence gives rise to unbounded Hopf branches that can produce secondary period-doubling bifurcations. Our results show that multiple stable periodic solutions can co-exist in certain parameter regions.

 

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