Nontrivial periodic solution for a stochastic brucellosis model with application to Xinjiang, China

2018 ◽  
Vol 510 ◽  
pp. 522-537 ◽  
Author(s):  
Lei Wang ◽  
Kai Wang ◽  
Daqing Jiang ◽  
Tasawar Hayat
Keyword(s):  
Periodic Solution ◽  
Nontrivial Periodic Solution

Dynamics and Optimal Control of a Monod–Haldane Predator–Prey System with Mixed Harvesting

2020 ◽  
Vol 30 (16) ◽  
pp. 2050243
Author(s):  
Xinxin Liu ◽  
Qingdao Huang
Keyword(s):  
Optimal Control ◽  
Periodic Solution ◽  
Local Stability ◽  
Maximum Yield ◽  
Multiple Shooting ◽  
Boundedness Of Solutions ◽  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Nontrivial Periodic Solution

This paper investigates the dynamics and optimal control of the Monod–Haldane predator–prey system with mixed harvesting that combines both continuous and impulsive harvestings. The periodic solution of the prey-free is studied and the local stability condition is obtained. The boundedness of solutions, the permanence of the system, and the existence of nontrivial periodic solution are studied. With the change of parameters, the system appears with a stable nontrivial periodic solution when the prey-free periodic solution loses stability. Numerical simulations show that the system has complex dynamical behaviors via bifurcation diagrams. Further, the maximum yield problem of the harvested system is studied, which is transformed into a nonlinear programming problem and solved by the method of combined multiple shooting and collocation.

Mathematical Analysis of Stability of a Spinning Disk Under Rotating, Arbitrarily Large Damping Forces

1996 ◽  
Vol 118 (4) ◽  
pp. 657-662 ◽  
Author(s):  
F. Y. Huang ◽  
C. D. Mote
Keyword(s):  
Periodic Solution ◽  
Parameter Space ◽  
Perturbation Technique ◽  
Stability Boundary ◽  
Rotating Disk ◽  
Stable Region ◽  
Damping Force ◽  
Analysis Of Stability ◽  
The Stability ◽  
Nontrivial Periodic Solution

Stability of a rotating disk under rotating, arbitrarily large damping forces is investigated analytically. Points possibly residing on the stability boundary are located exactly in parameter space based on the criterion that at least one nontrivial periodic solution is necessary at every boundary point. A perturbation technique and the Galerkin method are used to predict whether these points of periodic solution reside on the stability boundary, and to identify the stable region in parameter space. A nontrivial periodic solution is shown to exist only when the damping does not generate forces with respect to that solution. Instability occurs when the wave speed of a mode in the uncoupled disk, when observed on the disk, is exceeded by the rotation speed of the damping force relative to the disk. The instability is independent of the magnitude of the force and the type of positive-definite damping operator in the applied region. For a single dashpot, nontrivial periodic solutions exist at the points where the uncoupled disk has repeated eigenfrequencies on a frame rotating with the dashpot and the dashpot neither damps nor energizes these modes substantially around these points.

Nontrivial periodic solution of a stochastic non-autonomous SISV epidemic model

2016 ◽  
Vol 462 ◽  
pp. 837-845 ◽  
Author(s):  
Qun Liu ◽  
Daqing Jiang ◽  
Ningzhong Shi ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Periodic Solution ◽  
Epidemic Model ◽  
Nontrivial Periodic Solution

scholarly journals Dynamics for a stochastic delayed SIRS epidemic model

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Xiangyun Shi ◽  
Yimeng Cao ◽  
Xueyong Zhou
Keyword(s):  
Periodic Solution ◽  
Seasonal Variation ◽  
Global Existence ◽  
Positive Solutions ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sirs Epidemic Model ◽  
Nontrivial Periodic Solution ◽  
Well Posed ◽  
Disease Free

In this paper, we consider a stochastic delayed SIRS epidemic model with seasonal variation. Firstly, we prove that the system is mathematically and biologically well-posed by showing the global existence, positivity and stochastically ultimate boundneness of the solution. Secondly, some sufficient conditions on the permanence and extinction of the positive solutions with probability one are presented. Thirdly, we show that the solution of the system is asymptotical around of the disease-free periodic solution and the intensity of the oscillation depends of the intensity of the noise. Lastly, the existence of stochastic nontrivial periodic solution for the system is obtained.

Nontrivial periodic solution of a stochastic seasonal rabies epidemic model

2020 ◽  
Vol 545 ◽  
pp. 123361
Author(s):  
Zhongwei Cao ◽  
Wei Feng ◽  
Xiangdan Wen ◽  
Li Zu ◽  
Jinyao Gao
Keyword(s):  
Periodic Solution ◽  
Epidemic Model ◽  
Nontrivial Periodic Solution

Qualitative investigation of the second order equation x¨+f(x, x¯) x¯+g(x)=0

1997 ◽  
Vol 122 (2) ◽  
pp. 325-342 ◽  
Author(s):  
J. F. JIANG
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Order Equation ◽  
Second Order ◽  
Asymptotically Stable ◽  
Qualitative Investigation ◽  
Qualitative Behaviour ◽  
Globally Asymptotically Stable ◽  
All Solutions ◽  
Nontrivial Periodic Solution

This paper investigates the qualitative behaviour of solutions of the second order equation x¨+f(x, x¯) x¯+g(x)=0. The sufficient conditions for all solutions to be oscillatory are established. The theorems on the existence of a nontrivial periodic solution are proved and the criteria for the origin to be a global centre and globally asymptotically stable are given.

scholarly journals Analyzing a generalized pest-natural enemy model with nonlinear impulsive control

2018 ◽  
Vol 16 (1) ◽  
pp. 1390-1411 ◽  
Author(s):  
Changtong Li ◽  
Sanyi Tang
Keyword(s):  
Periodic Solution ◽  
Global Stability ◽  
Pest Control ◽  
Natural Enemy ◽  
Impulsive Control ◽  
Resource Limitation ◽  
Positive Periodic Solution ◽  
Wide Range ◽  
Holling Ii Functional Response ◽  
Nontrivial Periodic Solution

AbstractDue to resource limitation, nonlinear impulsive control tactics related to integrated pest management have been proposed in a generalized pest-natural enemy model, which allows us to address the effects of nonlinear pulse control on the dynamics and successful pest control. The threshold conditions for the existence and global stability of pest-free periodic solution are provided by Floquet theorem and analytic methods. The existence of a nontrivial periodic solution is confirmed by showing the existence of nontrivial fixed point of the stroboscopic mapping determined by time snapshot, which equals to the common impulsive period. In order to address the applications of generalized results and to reveal how the nonlinear impulses affect the successful pest control, as an example the model with Holling II functional response function is investigated carefully. The main results reveal that the pest free periodic solution and a stable interior positive periodic solution can coexist for a wide range of parameters, which indicates that the local stability does not imply the global stability of the pest free periodic solution when nonlinear impulsive control is considered, and consequently the resource limitation (i.e. nonlinear control) may result in difficulties for successful pest control.

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