Extinction, persistence and global stability in models of population growth (original) (raw)
2005, Journal of Mathematical Analysis and Applications
First, we systematize earlier results on the global stability of discrete model A n+1 = λA n + F (A n−m ) of population growth. Second, we invent the effect of delay m when F is unimodal. New, deep and strong results are discussed in Section 4, although Theorems 3-5 (Section 3) are still freshly new. This paper may be considered as a discrete version of our earlier work on the model x(t) = −µx(t) + f (x(t − τ )) [D.V. Giang, Y. Lenbury, Nonlinear delay differential equations involving population growth, Math. Comput. Modelling 40 (2004) 583-590]. We are mainly using ω-limit set of persistent solution, which is discussed in more general by P. Walters [An Introduction to Ergodic Theory, Springer-Verlag, Berlin, 1982].
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