Stability on a patch-structured Nicholson's blowflies system incorporating mature delay and feedback delay

ABSTRACT

In this paper, we focus on a patch-structured Nicholson's blowflies system incorporating mature delay and feedback delay. First, by exploiting the differential inequality technique, fluctuation lemma and Brouwer fixed point theorem, we obtain the persistence and existence of the positive equilibrium point with different components. Second, we develop an approach to establish some new criteria to guarantee the local stability and global attractivity of the positive equilibrium point vector, which complement and improve some existing results. Last, the effectiveness and feasibility of the theoretical results are illustrated by some computer simulations.

KEYWORDS:

• Nicholson's blowflies system
• positive equilibrium point
• stability
• attractivity
• patch structure
• delay

MR(2010) SUBJECT CLASSIFICATIONS:

• 34C25
• 34K13
• 34K25

Disclosure statement

No potential conflict of interest was reported by the author.