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 ) .

scholarly journals On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Haitao Li ◽  
Yansheng Liu
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Operator Theory ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Mixed Monotone Operator ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
Monotone Operator Theory ◽  
Delay Differential

This paper investigates a class of delay differential systems with feedback control. Sufficient conditions are obtained for the existence and uniqueness of the positive periodic solution by utilizing some results from the mixed monotone operator theory. Meanwhile, the dependence of the positive periodic solution on the parameterλis also studied. Finally, an example together with numerical simulations is worked out to illustrate the main results.

scholarly journals Synchronized Tick Population Oscillations Driven by Host Mobility and Spatially Heterogeneous Developmental Delays Combined

2021 ◽  
Vol 83 (6) ◽  
Author(s):  
Xue Zhang ◽  
Jianhong Wu
Keyword(s):  
Delay Differential Equations ◽  
Developmental Delays ◽  
Coupled System ◽  
Single Species ◽  
Adult Tick ◽  
Life Cycles ◽  
Positive Equilibrium ◽  
Tick Population ◽  
Host Mobility ◽  
Delay Differential

AbstractWe consider a coupled system of delay differential equations for a single-species tick population dynamics, assuming feeding adult ticks are distributed by their hosts in a spatially heterogeneous environment consisting of two patches where egg ticks produced will complete their life cycles with different, normal and diapause, developmental delays. We show that the mobility of adult tick host and the diapause developmental delay combined drive a synchronized oscillation in the total tick populations around a uniquely defined positive equilibrium, and this synchronization makes the oscillatory patterns much simpler in comparison with multi-peak oscillations exhibited in the absence of host mobility.

scholarly journals Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Nattawut Khansai ◽  
Akapak Charoenloedmongkhon
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Control ◽  
Positive Periodic Solution ◽  
Existence Condition ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Behavior

AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

Sign in / Sign up

Export Citation Format

Share Document