Novel stability criteria on a patch structure Nicholson's blowflies model with multiple pairs of time-varying delays

Xin Long; Xin Long

doi:10.3934/math.2020473

AIMS Mathematics

2020, Volume 5, Issue 6: 7387-7401. doi: 10.3934/math.2020473

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Research article

Novel stability criteria on a patch structure Nicholson's blowflies model with multiple pairs of time-varying delays

Xin Long ^,

School of Mathematics and Statistics, Changsha University of Science and Technology; Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, China

Received: 07 August 2020 Accepted: 08 September 2020 Published: 21 September 2020
MSC : 34K13, 34C25

This paper investigates a patch structure Nicholson's blowflies model involving multiple pairs of different time-varying delays. Without assuming the uniform positiveness of the death rate and the boundedness of coefficients, we establish three novel criteria to check the global convergence, generalized exponential convergence and asymptotical stability on the zero equilibrium point of the addressed model, respectively. Our proofs make substantial use of differential inequality techniques and dynamical system approaches, and the obtained results improve and supplement some existing ones. Last but not least, a numerical example with its simulations is given to show the feasibility of the theoretical results.
- patch structure,
- Nicholson's blowflies model,
- convergence,
- asymptotical stability,
- time-varying delay
Citation: Xin Long. Novel stability criteria on a patch structure Nicholson's blowflies model with multiple pairs of time-varying delays[J]. AIMS Mathematics, 2020, 5(6): 7387-7401. doi: 10.3934/math.2020473

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Abstract

This paper investigates a patch structure Nicholson's blowflies model involving multiple pairs of different time-varying delays. Without assuming the uniform positiveness of the death rate and the boundedness of coefficients, we establish three novel criteria to check the global convergence, generalized exponential convergence and asymptotical stability on the zero equilibrium point of the addressed model, respectively. Our proofs make substantial use of differential inequality techniques and dynamical system approaches, and the obtained results improve and supplement some existing ones. Last but not least, a numerical example with its simulations is given to show the feasibility of the theoretical results.

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