scholarly journals Synchronization control of stochastic delayed Lotka–Volterra systems with hardware simulation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lan Wang ◽  
Yiping Dong ◽  
Da Xie ◽  
Hao Zhang
Keyword(s):  
Sufficient Conditions ◽  
Synchronization Control ◽  
Simulation Tool ◽  
Volterra System ◽  
Stochastic Effects ◽  
Volterra Systems ◽  
Field Programmable ◽  
Global Positive Solution ◽  
System With Time Delay ◽  
Theoretical Results

AbstractIn this paper, the synchronization control of a non-autonomous Lotka–Volterra system with time delay and stochastic effects is studied. The purpose is to firstly establish sufficient conditions for the existence of global positive solution by constructing a suitable Lyapunov function. Some synchronization criteria are then derived by designing an appropriate full controller and a pinning controller, respectively. Finally, an example is presented to illustrate the feasibility and validity of the main theoretical results based on the Field-Programmable Gate Array hardware simulation tool.

Stability in distribution of stochastic Lotka–Volterra delay system under regime switching

2018 ◽  
Vol 18 (05) ◽  
pp. 1850041
Author(s):  
Yanchao Zang ◽  
Pingjun Hou ◽  
Yuzhu Tian
Keyword(s):  
Regime Switching ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Classical Case ◽  
Delay System ◽  
Global Positive Solution ◽  
Stability In Distribution ◽  
The Stability ◽  
System With Time Delay ◽  
Theoretical Results

In this paper, we consider a class of stochastic competitive Lotka–Volterra system with time delay and Markovian switching. We prove that there exists a global positive solution under the random perturbation. Some sufficient conditions for the stability in distribution of the system are established which improved the classical case. An example is given to illustrate theoretical results.

scholarly journals Chaos in perturbed Lotka-Volterra systems

2001 ◽  
Vol 42 (3) ◽  
pp. 399-412
Author(s):  
J. R. Christie ◽  
K. Gopalsamy ◽  
Jibin Li
Keyword(s):  
Sufficient Conditions ◽  
Chaotic Behaviour ◽  
Volterra Equations ◽  
Unperturbed System ◽  
Heteroclinic Cycle ◽  
Volterra System ◽  
Perturbed System ◽  
Volterra Systems ◽  
Perturbed Systems ◽  
Special Case

AbstractLotka-Volterra systems have been used extensively in modelling population dynamics. In this paper, it is shown that chaotic behaviour in the sense of Smale can exist in timeperiodically perturbed systems of Lotka-Volterra equations. First, a slowly varying threedimensional perturbed Lotka-Volterra system is considered and the corresponding unperturbed system is shown to possess a heteroclinic cycle. By using Melnikov's method, sufficient conditions are obtained for the perturbed system to have a transverse heteroclinic cycle and hence to possess chaotic behaviour in the sense of Smale. Then a special case involving a reduction to a two-dimensional Lotka-Volterra system is examined, leading finally to an application with a model for the self-organisation of macromolecules.

scholarly journals Dynamics of a stochastic HIV/AIDS model with treatment under regime switching

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Miaomiao Gao ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Stationary Distribution ◽  
Regime Switching ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Aids Model ◽  
Telegraph Noise ◽  
Spread Dynamics ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Hiv Aids

<p style='text-indent:20px;'>This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.</p>

Dynamics of a stochastic rabies epidemic model with markovian switching

2021 ◽  
pp. 2150032
Author(s):  
Hao Peng ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Lyapunov Function ◽  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Telegraph Noise ◽  
Global Positive Solution ◽  
Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

scholarly journals Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 745 ◽  
Author(s):  
Tongqian Zhang ◽  
Tingting Ding ◽  
Ning Gao ◽  
Yi Song
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Influenza A ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

scholarly journals Dynamics of a single predator multiple prey model with stochastic perturbation and seasonal variation

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 535-549
Author(s):  
Hong-Wen Hui ◽  
Lin-Fei Nie
Keyword(s):  
Seasonal Variation ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Analysis Method ◽  
Ultimate Boundedness ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
Stochastically Ultimate Boundedness ◽  
Theoretical Results

Considering various factors are stochastic rather than deterministic in the evolution of populations growth, in this paper, we propose a single predator multiple prey stochastic model with seasonal variation. By using the method of solving an explicit solution, the existence of global positive solution of this model are obtained. The method is more convenient than Lyapunov analysis method for some population models. Moreover, the stochastically ultimate boundedness are considered by using the comparison theorem of stochastic differential equation. Further, some sufficient conditions for the extinction and strong persistence in the mean of populations are discussed, respectively. In addition, by constructing some suitable Lyapunov functions, we show that this model admits at least one periodic solution. Finally, numerical simulations clearly illustrate the main theoretical results and the effects of white noise and seasonal variation for the persistence and extinction of populations.

PERSISTENCE AND GLOBAL STABILITY IN A PREDATOR-PREY SYSTEM WITH DELAY

2006 ◽  
Vol 16 (10) ◽  
pp. 2915-2922 ◽  
Author(s):  
MANUEL GÁMEZ ◽  
CLOTILDE MARTÍNEZ
Keyword(s):  
Time Delay ◽  
Autonomous Systems ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Lyapunov Functionals ◽  
Volterra System ◽  
Predator Prey ◽  
Prey System ◽  
Necessary And Sufficient ◽  
System With Time Delay

In this paper, several sufficient conditions are established for the persistence and extinction in a Lotka–Volterra system with time delay. Based on the use of Lyapunov functionals techniques, necessary and sufficient conditions are also given for global asymptotic stability of the positive equilibrium for autonomous systems.

Stochastic properties of solution for a chemostat model with a distributed delay and random disturbance

2020 ◽  
Vol 13 (07) ◽  
pp. 2050066
Author(s):  
Xiaofeng Zhang ◽  
Rong Yuan
Keyword(s):  
Linear Chain ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Degenerate System ◽  
Random Disturbance ◽  
Chemostat Model ◽  
Boundary Equilibrium ◽  
Global Positive Solution ◽  
Stochastic Properties ◽  
Theoretical Results

In this paper, stochastic properties of solution for a chemostat model with a distributed delay and random disturbance are studied, and we use distribution delay to simulate the delay in nutrient conversion. By the linear chain technique, we transform the stochastic chemostat model with weak kernel into an equivalent degenerate system which contains three equations. First, we state that this model has a unique global positive solution for any initial value, which is helpful to explore its stochastic properties. Furthermore, we prove the stochastic ultimate boundness of the solution of system. Then sufficient conditions for solution of the system tending toward the boundary equilibrium point at exponential rate are established, which means the microorganism will be extinct. Moreover, we also obtain some sufficient conditions for ergodicity of solution of this system by constructing some suitable stochastic Lyapunov functions. Finally, we provide some numerical examples to illustrate theoretical results, and some conclusions and analysis are given.

N-intertwined SIS epidemic model with Markovian switching

2019 ◽  
Vol 19 (04) ◽  
pp. 1950031 ◽  
Author(s):  
Xiaochun Cao ◽  
Zhen Jin
Keyword(s):  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Sis Model ◽  
Color Noise ◽  
Epidemic Dynamics ◽  
Sis Epidemic Model ◽  
Finite State ◽  
Global Positive Solution ◽  
Time Average ◽  
Theoretical Results

Epidemic dynamics is often subject to environmental noise and uncertainty. In this paper, we investigate the effect of color noise on the spread of epidemic in complex networks, which is modeled by stochastic switched differential equations based on the [Formula: see text]-intertwined SIS model using a continuous time finite-state Markov chain. Applying Lyapunov functions, we prove that the model has a unique global positive solution and establish sufficient conditions for stochastic extinction and permanence of the epidemic. We also show that the solution is stochastically ultimately bounded and the variance of the solution is bounded too. Furthermore, we discuss the limit of the time average of the solution. Finally, numerical simulations are carried out to illustrate our theoretical results.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

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