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Themain theme of this chapter is to study the instability characteristics of the model equations induced by time delays. We have established in Chap. 1 that the basic model (1.5) is structurally stable. Also when the average time delays are sufficiently small, results are obtained for the boundedness of solutions, and local and global stability of equilibria of the models of Chap. 2 by restricting the other parameters of these systems. But we have noticed in Sect. 2.3 that in the presence of a time delay in growth response, the system tends to lose its stability leading to Hopf bifurcation. We have not discussed this aspect in case of other models such as (2.29).
KeywordsHopf Bifurcation Growth Response Positive Equilibrium Material Recycling Positive Real Part
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