Global existence and stability of Nicholson blowflies model with harvesting and random effect

A generalized Nicholson blowflies model with harvesting or immigration and random effect is considered. We discuss the existence of positive global solution and provide the estimate on the lower bound of the Lyapunov exponent. Moreover, we show that the nontrivial equilibrium solution is mean square...

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Bibliographic Details
Published inNonlinear dynamics Vol. 103; no. 2; pp. 2109 - 2123
Main Authors Abbas, Syed, Niezabitowski, Michal, Grace, Said R.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 2021
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Liapunov exponents
Lower bounds
Mathematical models
Mechanical Engineering
Original Paper
Stability
Vibration
Brownian motion
Lyapunov functional
Stochastic stability
Nicholson model
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Summary:A generalized Nicholson blowflies model with harvesting or immigration and random effect is considered. We discuss the existence of positive global solution and provide the estimate on the lower bound of the Lyapunov exponent. Moreover, we show that the nontrivial equilibrium solution is mean square exponential stability and stable in probability. We prove several results using techniques of stochastic calculus. It is evident from the obtained conditions that the noise plays an important role in all qualitative properties of the solution. Numerical simulations are also provided in order to validate the analytical findings. The results are new and compliments the existing ones.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-06196-z