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島根大学理学部紀要 23 巻
1989-12-25 発行
遅れ型微分方程式N^^・(t)=N(t)(a-bN(t-1)-cN(t-2))について
On the delay-differential equation N^^・(t)=N(t)(a-bN(t-1)-cN(t-2))
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Boundedness and asymptotic behavior of solutions and existence of periodic solutions of the scalar generalized logistic equation N^^・(t) = N(t) (a - bN(t - 1) - cN(t - 2)) are discussed. In particular, we show partial global uniform asymptotic stability of the constant solution N (t) = a/(b + c), and existence of nontrivial periodic solutions by using a Hopf bifurcation and a fixed point theorem for a closed convex set.
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