Persistence and periodic solutions in systems of delay differential equations

作者：

Highlights：

• Systems of non-autonomous delayed differential equations are considered.

• Guiding functions techniques are employed to prove the weak and strong persistence. Stronger assumptions allow to prove uniform persistence.

• Periodic solutions are obtained via topological degree methods.

• When the conditions for persistence are not fulfilled, an extra assumption implies that the trivial equilibrium is a global attractor.

摘要

•Systems of non-autonomous delayed differential equations are considered.•Guiding functions techniques are employed to prove the weak and strong persistence. Stronger assumptions allow to prove uniform persistence.•Periodic solutions are obtained via topological degree methods.•When the conditions for persistence are not fulfilled, an extra assumption implies that the trivial equilibrium is a global attractor.

论文关键词：Delay differential equations,Semi-dynamical systems,Persistence,Guiding functions,Periodic solutions,Topological degree,Global attractor

论文评审过程：Received 21 January 2020, Revised 26 February 2021, Accepted 9 March 2021, Available online 23 March 2021, Version of Record 23 March 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126193