Periodicity and multi-periodicity generated by impulses in delayed differential inclusions: application to discontinuous Nicholson’s blowflies model. (English) Zbl 1430.34024
Summary: Based on Krasnoselskii’s fixed point theorem of set-valued maps type, this paper studies the existence and multiplicity of periodic positive solutions for delayed differential inclusions with impulsive effects. These periodic positive solutions are generated by impulses. Then, the obtained results are applied to delayed Nicholson’s blowflies model where a novel discontinuous stocking policy is proposed. These results are of great significance in maintaining the sustainable development for populations, especially for endangered populations in a biological system.
MSC:
| 34A60 | Ordinary differential inclusions |
| 34K09 | Functional-differential inclusions |
| 34K45 | Functional-differential equations with impulses |
| 34A37 | Ordinary differential equations with impulses |
| 37N25 | Dynamical systems in biology |
| 92D25 | Population dynamics (general) |
Keywords:
delayed differential inclusion; periodicity; multi-periodicity; impulses; Nicholson’s blowflies model; discontinuous stocking policyReferences:
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