scholarly journals Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Liang Zhao ◽  
Bin Qin ◽  
Fengde Chen
Keyword(s):  
Comparison Theorem ◽  
Crucial Role ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Toxic Substances ◽  
Feedback Controls ◽  
Infinite Delays

A discrete allelopathic phytoplankton model with infinite delays and feedback controls is studied in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantees the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the extinction of the system are obtained. Our results extend and supplement some known results and show that the feedback controls and toxic substances play a crucial role on the permanence and extinction of the system.

scholarly journals The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 173 ◽  
Author(s):  
Liang Zhao ◽  
Fengde Chen ◽  
Saixi Song ◽  
Guizhen Xuan
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Difference Equations ◽  
Crucial Role ◽  
Sufficient Conditions ◽  
Toxic Substances ◽  
Competitive System ◽  
Feedback Controls

A non-autonomous allelopathic phytoplankton model with nonlinear inter-inhibition terms and feedback controls is studied in this paper. Based on the comparison theorem of differential equation, some sufficient conditions for the permanence of the system are obtained. We study the extinction of one of the species by using some suitable Lyapunov type extinction function. Our analyses extend those of Xie et al. (Extinction of a two species competitive system with nonlinear inter-inhibition terms and one toxin producing phytoplankton. Advances in Difference Equations, 2016, 2016, 258) and show that the feedback controls and toxic substances have no effect on the permanence of the system but play a crucial role on the extinction of the system. Some known results are extended.

scholarly journals Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Liang Zhao ◽  
Xiangdong Xie ◽  
Liya Yang ◽  
Fengde Chen
Keyword(s):  
Biological Control ◽  
Feedback Control ◽  
Comparison Theorem ◽  
Global Attractivity ◽  
Control Variable ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Competitive System ◽  
Competition System ◽  
Infinite Delays

A nonautonomous discrete two-species Lotka-Volterra competition system with infinite delays and single feedback control is considered in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that if the the discrete Lotka-Volterra competitive system with infinite delays and without feedback control is permanent, then, by choosing some suitable feedback control variable, the permanent species will be driven to extinction. That is, the feedback control variable, which represents the biological control or some harvesting procedure, is the unstable factor of the system. Such a finding overturns the previous scholars’ recognition on feedback control variables.

scholarly journals Global Attractivity and Extinction of a Discrete Competitive System with Infinite Delays and Single Feedback Control

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Yalong Xue ◽  
Xiangdong Xie ◽  
Qifa Lin ◽  
Fengde Chen
Keyword(s):  
Feedback Control ◽  
Comparison Theorem ◽  
Global Attractivity ◽  
Control Variable ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Species Competition ◽  
Competitive System ◽  
Competition System ◽  
Infinite Delays

A nonautonomous discrete two-species competition system with infinite delays and single feedback control is considered in this paper. Based on the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Then, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that, by choosing some suitable feedback control variable, one of two species will be driven to extinction.

PERMANENCE IN NONAUTONOMOUS DISCRETE LOTKA–VOLTERRA n-SPECIES COMPETITIVE SYSTEMS WITH PURE-DELAYS AND FEEDBACK CONTROLS

2013 ◽  
Vol 24 (07) ◽  
pp. 1350053 ◽  
Author(s):  
AHMADJAN MUHAMMADHAJI ◽  
ZHIDONG TENG ◽  
LINFEI NIE
Keyword(s):  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Feedback Controls ◽  
Volterra Type ◽  
Competitive Systems ◽  
Analysis Technique

The paper discusses nonautonomous discrete Lotka–Volterra type n-species competitive systems with pure-delays and feedback controls. New sufficient conditions for which a part of the n-species remains permanent and others is driven to extinction are established by using the method of multiple discrete Lyapunov functionals and introducing new analysis technique. Our results show that the feedback controls cannot influence the permanence of species.

Extinction in a discrete Lotka–Volterra competitive system with the effect of toxic substances and feedback controls

2015 ◽  
Vol 08 (01) ◽  
pp. 1550012 ◽  
Author(s):  
Lijuan Chen ◽  
Fengde Chen
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
The Other ◽  
Toxic Substances ◽  
Two Dimensional ◽  
Competitive System ◽  
Feedback Controls ◽  
Analysis Technique

In this paper, we consider a discrete Lotka–Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka–Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 (2008) 165–178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.

scholarly journals Extinction in Nonautonomous Discrete Lotka-Volterra Competitive System with Pure Delays and Feedback Controls

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
Ling Zhang ◽  
Zhidong Teng ◽  
Tailei Zhang ◽  
Shujing Gao
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Competitive System ◽  
Feedback Controls

The paper discusses a nonautonomous discrete time Lotka-Volterra competitive system with pure delays and feedback controls. New sufficient conditions for which a part of then-species is driven to extinction are established by using the method of multiple discrete Lyapunov functionals.

PERMANENCE OF A DISCRETE n-SPECIES LOTKA–VOLTERRA TYPE FOOD-CHAIN SYSTEM WITH FEEDBACK CONTROLS AND TIME DELAYS

2008 ◽  
Vol 01 (03) ◽  
pp. 299-311 ◽  
Author(s):  
XUMING HUANG ◽  
WENSHENG YANG ◽  
XUEPENG LI
Keyword(s):  
Difference Equation ◽  
Comparison Theorem ◽  
Food Chain ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Volterra Type ◽  
Chain System

In this paper, a discrete n-species Lotka–Volterra type food-chain system with time delays and feedback controls is proposed. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.

scholarly journals Permanence of a Discrete Predator-Prey Systems with Beddington-DeAngelis Functional Response and Feedback Controls

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Xuepeng Li ◽  
Wensheng Yang
Keyword(s):  
Difference Equation ◽  
Functional Response ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Predator Prey

We propose a discrete predator-prey systems with Beddington-DeAngelis functional response and feedback controls. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.

Availability and accessibility of medications and toxic substances and suicidal behavior

2016 ◽  
Vol 33 (S1) ◽  
pp. S596-S596
Author(s):  
M. Arsenyan ◽  
S. Sukiasyan ◽  
T. Hovhannisyan
Keyword(s):  
Suicidal Behavior ◽  
Significant Influence ◽  
Crucial Role ◽  
Attempted Suicide ◽  
Conflict Situation ◽  
Toxic Substances ◽  
Suicide Method ◽  
Teenage Girls ◽  
Competing Interest ◽  
Suicidal Crisis

IntroductionScientific research indicates that accessibility of suicide means has a significant influence on the choice of method. Since the choice of suicide method largely depends on availability of suicide means, the lethality of method at hand plays a crucial role in a period of suicidal crisis.AimsWe aimed to reveal the associations between accessibility and availability of medications and toxic substances and suicidal behavior of teenage girls in Armenia.ObjectiveOur objectives were to determine whether accessibility and availability of medications and toxic substances have any impact on development of suicidal behavior among teenage girls in Armenia and whether toxicity and quantity of medications and toxic substances at hand or purchased by attempters are associated with severity of outcome.MethodsA qualitative analysis of patient histories of 26 teenage girls, hospitalized in the ICU, Toxicology Center “Muratsan”, Yerevan, RA, diagnosed as having acute deliberate self-poisoning was performed.ResultsIn majority of cases, conflict situation preceded suicidal behavior and decision on attempting suicide was impulsive. Being emotionally distressed teenage girls reached for medications and toxic substances readily available in the household or bought medications from a pharmacy.ConclusionThe vast majority of teenage girls attempted suicide by medications and toxic substances at hand. Admittedly, both, type of medication and quantity of pills or amount of toxic substances utilized, affected the severity of outcome. Hence, the availability and accessibility of medications and toxic substances played a crucial role in development of suicidal behavior and severity of outcome.Disclosure of interestThe authors have not supplied their declaration of competing interest.

scholarly journals Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Caifeng Du
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

Sign in / Sign up

Export Citation Format

Share Document