Global dynamics of delay equations for populations with competition among immature individuals. (English) Zbl 1337.34080
By the notion of strong attractor the authors reduce the study of the attracting properties of the equilibria of the DDEs
\[
u'_1(t)=P_1(b_1(u_1(t-\tau),u_2(t-\tau)),b_2(u_1(t-\tau),u_2(t-\tau)))-\mu_1 u_1(t),
\]
\[ u'_2(t)=P_1(b_1(u_1(t-\tau),u_2(t-\tau)),b_2(u_1(t-\tau),u_2(t-\tau)))-\mu_2 u_2(t) \] to the analysis of a related two-dimensional discrete system.
Explicit easily verifiable conditions are obtained for global extinction and global attractivity for planar Lotka-Volterra systems.
\[ u'_2(t)=P_1(b_1(u_1(t-\tau),u_2(t-\tau)),b_2(u_1(t-\tau),u_2(t-\tau)))-\mu_2 u_2(t) \] to the analysis of a related two-dimensional discrete system.
Explicit easily verifiable conditions are obtained for global extinction and global attractivity for planar Lotka-Volterra systems.
Reviewer: Leonid Berezanski (Beer-Sheva)
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 39A10 | Additive difference equations |
| 92D25 | Population dynamics (general) |
| 34K25 | Asymptotic theory of functional-differential equations |
Keywords:
age structured population; delay differential equations; global attractor; competition; monotone planar maps; Lotka-Volterra systemsReferences:
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