Stationary distribution and periodic solution of a stochastic Nicholson's blowflies model with distributed delay

2021 ◽  
Author(s):  
Xiaojie Mu ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Periodic Solution ◽  
Stationary Distribution ◽  
Distributed Delay ◽  
Nicholson’S Blowflies Model

Periodic Solution of a Stochastic Microorganism Flocculation Model with Distributed Delay

2021 ◽  
Author(s):  
Xiaojie Mu ◽  
Daqing Jiang
Keyword(s):  
Periodic Solution ◽  
Dynamic Change ◽  
Distributed Delay ◽  
Positive Periodic Solution ◽  
Point Of View ◽  
Ocean Current ◽  
Positive Equilibrium ◽  
Microorganism Population ◽  
External Conditions ◽  
Delay Differential

Abstract In this paper, a nonautonomous delay differential equation of microorganism flocculation is established by considering the influence of external conditions such as seasonal alternation and ocean current movement on the ecological function of microorganism population. At the same time, the dynamic change characteristics of microorganism population in oil spill environment were simulated, and on this basis, the effects of diurnal change and climate change on the parameters of microorganism system were analyzed. From a mathematical point of view, the stochastic microorganism flocculation model exists a T-positive periodic solution. The existence and uniqueness of globally positive equilibrium of the exploited model is studied. Finally, some numerical examples illustrate the results.

scholarly journals On Periodic Solutions of Delay Differential Equations with Impulses

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 523 ◽  
Author(s):  
Mostafa Bachar
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Distributed Delay ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential ◽  
Distributed Delay Differential Equations

The purpose of this paper is to study the nonlinear distributed delay differential equations with impulses effects in the vectorial regulated Banach spaces R ( [ − r , 0 ] , R n ) . The existence of the periodic solution of impulsive delay differential equations is obtained by using the Schäffer fixed point theorem in regulated space R ( [ − r , 0 ] , R n ) .

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