New results on stability of Nicholson's blowflies equation with multiple pairs of time-varying delays

Abstract This paper is concerned with a non-autonomous Nicholson’s blowflies equation with multiple pairs of time-varying delays. By using differential inequality techniques and the fluctuation lemma, we establish two criteria on the global exponential stability and global asymptotical stability on the zero equilibrium of the addressed equation, respectively. The obtained results improve and complement some existing ones. The effectiveness of the obtained results is illustrated by some numerical simulations.

[1]  Elena Braverman,et al.  A note on stability of Mackey–Glass equations with two delays , 2017 .

[2]  Lihong Huang,et al.  Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term , 2019, Communications on Pure & Applied Analysis.

[3]  Igor Simone Stievano,et al.  Topological modelling of gas networks for co-simulation applications in multi-energy systems , 2021, Math. Comput. Simul..

[4]  Hal L. Smith,et al.  An introduction to delay differential equations with applications to the life sciences / Hal Smith , 2010 .

[5]  Hien Le,et al.  Global attractivity of positive periodic solution of a delayed Nicholson model with nonlinear density-dependent mortality term , 2019, Electronic Journal of Qualitative Theory of Differential Equations.

[6]  Hassan A. El-Morshedy,et al.  Global convergence to equilibria in non-monotone delay differential equations , 2019, Proceedings of the American Mathematical Society.

[7]  Jinde Cao,et al.  Stability and Hopf Bifurcation of a Delayed Prey-Predator Model with Disease in the Predator , 2019, Int. J. Bifurc. Chaos.

[8]  Elena Braverman,et al.  Nicholson's blowflies differential equations revisited: Main results and open problems , 2010 .

[9]  Yanling Zhu,et al.  Stochastic Nicholson's blowflies delay differential equation with regime switching , 2019, Appl. Math. Lett..

[10]  Jinde Cao,et al.  Stability analysis of Nicholson's blowflies equation with two different delays , 2020, Math. Comput. Simul..

[11]  Wentao Wang,et al.  Stochastic Nicholson's blowflies delayed differential equations , 2019, Appl. Math. Lett..

[12]  Chuangxia Huang,et al.  On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities , 2014 .

[13]  Luogen Yao,et al.  Dynamics of Nicholson’s blowflies models with a nonlinear density-dependent mortality , 2018, Applied Mathematical Modelling.

[14]  Yanli Xu,et al.  New stability theorem for periodic Nicholson's model with mortality term , 2019, Appl. Math. Lett..

[15]  Bingwen Liu,et al.  Global exponential stability of positive periodic solutions for a delayed Nicholsonʼs blowflies model , 2014 .

[16]  Jinde Cao,et al.  Asymptotically stable high-order neutral cellular neural networks with proportional delays and D operators , 2020, Math. Comput. Simul..