Novel stability conditions for some generalization of Nicholson's blowflies model with stochastic perturbations

Leonid  Shaikhet; Syed Abbas

doi:10.21914/anziamj.v64.17420

Authors

Leonid Shaikhet Ariel University https://orcid.org/0000-0001-7354-1383
Syed Abbas Indian Institute of Technology Mandi

DOI:

https://doi.org/10.21914/anziamj.v64.17420

Keywords:

positive equilibrium, stochastic perturbations, white noise, stability in probability, Lyapunov functionals, Linear Matrix Inequality (LMI), numerical simulations

Abstract

We consider a generalization of the well-known nonlinear Nicholson blowflies model with stochastic perturbations. Stability in probability of the positive equilibrium of the considered equation is studied. Two types of stability conditions: delay-dependent and delay-independent conditions are obtained, using the method of Lyapunov functionals and the method of linear matrix inequalities. The obtained results are illustrated by numerical simulations by means of some examples. The results are new, and complement the existing ones.

doi: 10.1017/S1446181123000147

Author Biographies

Leonid Shaikhet, Ariel University

Department of Mathematics, Ariel University, Ariel 40700, Israel

Syed Abbas, Indian Institute of Technology Mandi

Chairperson, School of Basic Sciences, IIT Mandi;

School of Mathematical and Statistical Sciences, IIT Mandi, Mandi, H.P. 175005, India