Novel stability conditions for some generalization of Nicholson's blowflies model with stochastic perturbations
Keywords:positive equilibrium, stochastic perturbations, white noise, stability in probability, Lyapunov functionals, Linear Matrix Inequality (LMI), numerical simulations
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.