GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS

A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.

Positive Solutions Bifurcating from Zero Solution in a Lotka-Volterra Competitive System with Cross-Diffusion Effects

A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.

Dynamics of a Two Species Competitive System with Pure Delays

A class of non-autonomous two species Lotka-Volterra competitive system with pure discrete time delays is discussed. Some sufficient conditions on the boundedness, permanence, periodic solution and global attractivity of the system are established by means of the comparison method and Liapunov functional.

Periodic Solution for Stochastic Non-autonomous Schoener Competitive System

In this paper, we consider a stochastic non-autonomous Schoener competitive system. Firstly, we prove the existence of positive periodic solution when the coefficients of Schoener competitive system satisfied certain conditions. Then the global attractiveness of positive periodic solution is also proved by constructing appropriate Lyapunov function. In addition, we show that the stronger noises will lead to the extinction of competitive systems.

Existence of Two Limit Cycles in Zeeman’s Class 30 for 3D Lotka-Volterra Competitive System

Gyllenberg and Yan(Discrete Contin Dyn Syst Ser B 11(2):347–352,2009)presented a system in Zeeman’s class 30 of 3-dimensional Lotka-Volterra(3D LV)competitive systems to admit at least two limit cycles,one of which is generated by the Hopf bifurcation and the other is obtained by the Poincaré-Bendixson theorem.Yu et al.(J Math Anal Appl 436:521–555,2016,Sect.3.4)recalculated the first Liapunov coefficient of Gyllenberg and Yan’s system to be positive,rather than negative as in Gyllenberg and Yan(2009),and pointed out that the Poincaré-Bendixson theorem is not applicable for that system.Jiang et al.(J Differ Equ 284:183–218,2021,p.213)proposed an open question:“whether Zeeman’s class 30 can be rigorously proved to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem?”This paper provides four systems in Zeeman’s class 30 to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem and gives an answer to the above question.

Treatment of Helicobacter pylori with potassium competitive acid blockers:A systematic review and meta-analysis

BACKGROUND Helicobacter pylori(H.pylori)infects over half the global population,causing gastrointestinal diseases like dyspepsia,gastritis,duodenitis,peptic ulcers,GMALT lymphoma,and gastric adenocarcinoma.Eradicating H.pylori is crucial for treating and preventing these conditions.While conventional proton pump inhibitor(PPI)-based triple therapy is effective,there’s growing interest in longer acid suppression therapies.Potassium competitive acid blocker(P-CAB)triple and dual therapy are new regimens for H.pylori eradication.Initially used in Asian populations,vonoprazan(VPZ)has been recently Food and Drug Administration-approved for H.pylori eradication.AIM To assess the efficacy of regimens containing P-CABs in eradicating H.pylori infection.METHODS This study,following PRISMA 2020 guidelines,conducted a systematic review and meta-analysis by searching MEDLINE and Scopus libraries for randomized clinical trials(RCTs)or observational studies with the following command:[("Helicobacter pylori"OR"H pylori")AND("Treatment"OR"Therapy"OR"Eradication")AND("Vonaprazan"OR"Potassium-Competitive Acid Blocker"OR"P-CAB"OR"PCAB"OR"Revaprazan"OR"Linaprazan"OR"Soraprazan"OR"Tegoprazan")].Studies comparing the efficacy of P-CABs-based treatment to classical PPIs in eradicating H.pylori were included.Exclusion criteria included case reports,case series,unpublished trials,or conference abstracts.Data variables encompassed age,diagnosis method,sample sizes,study duration,intervention and control,and H.pylori eradication method were gathered by two independent reviewers.Meta-analysis was performed in R software,and forest plots were generated.RESULTS A total of 256 references were initially retrieved through the search command.Ultimately,fifteen studies(7 RCTs,7 retrospective observational studies,and 1 comparative unique study)were included,comparing P-CAB triple therapy to PPI triple therapy.The intention-to-treat analysis involved 8049 patients,with 4471 in the P-CAB intervention group and 3578 in the PPI control group across these studies.The analysis revealed a significant difference in H.pylori eradication between VPZ triple therapy and PPI triple therapy in both RCTs and observational studies[risk ratio(RR)=1.17,95%confidence interval(CI):1.11-1.22,P<0.0001]and(RR=1.13,95%CI:1.09-1.17,P<0.0001],respectively.However,no significant difference was found between tegoprazan(TPZ)triple therapy and PPI triple therapy in both RCTs and observational studies(RR=1.04,95%CI:0.93-1.16,P=0.5)and(RR=1.03,95%CI:0.97-1.10,P=0.3),respectively.CONCLUSION VPZ-based triple therapy outperformed conventional PPI-based triple therapy in eradicating H.pylori,positioning it as a highly effective first-line regimen.Additionally,TPZ-based triple therapy was non-inferior to classical PPI triple therapy.

A generalized stochastic competitive system with Ornstein-Uhlenbeck process

A generalized competitive system with stochastic perturbations is proposed in this paper,in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process.By theories of stochastic differential equations,such as comparison theorem,Ito’s integration formula,Chebyshev’s inequality,martingale’s properties,etc.,the existence and the uniqueness of global positive solution of the system are obtained.Then sufficient conditions for the extinction of the species almost surely,persistence in the mean and the stochastic permanence for the system are derived,respectively.Finally,by a series of numerical examples,the feasibility and correctness of the theoretical analysis results are verified intuitively.Moreover,the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.

Existence and global asymptotic stability of positive almost periodic solutions of a two-species competitive system

The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of posi- tive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results.

Dynamics behaviors of a delayed competitive system in a random environment

In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.

A Class of Singularly Perturbed Problems for Nonlinear Two-Species Competitive Reaction-Diffusion System

A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.

ON THE EXISTENCE AND UNIQUENESS OF ALMOST PERIODIC SOLUTIONS TO DISCRETE TWO-SPECIES COMPETITIVE SYSTEMS

In this paper, we consider almost periodic discrete two-species competitive sys-tems. By using Lyapunov functional, the existence conditions and uniqueness of almost periodic solutions for the this type of systems are obtained.

NOTE ON THE PARTIAL SURVIVAL OF A TWO SPECIES LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH INFINITE DELAYS AND FEEDBACK CONTROLS

A two species Lotka-Volterra competitive system with infinite delays and feedback controls is studied in this paper.By constructing a suitable Lyapunov functional,we show that if the Lotka-Volterra competitive system is bistable(in the absence of feedback controls),then by choosing some suitable values of feedback control variables,one of the species is driven to extinction while the other one becomes globally stable.Examples together with their numerical simulations are presented to verify the feasibility of our results.Our results not only improve but also complement those of Z.Li,M.A.Han and F.D.Chen[Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays,Nonlinear Anal.:Real World Appl.,14(2013),402-413].

EXTINCTION OF A DISCRETE COMPETITIVE SYSTEM WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE AND THE EFFECT OF TOXIC SUBSTANCES

In this paper, we consider a discrete competitive system with BeddingtonDe Angelis functional response and the effect of toxic substances. By constructing some suitable Lyapunov type extinction functions, sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. Our results not only supplement and improve but also generalize some existing ones. Numerical simulations show the feasibility of our results.

OPTIMAL IMPULSIVE CONTROL IN COMPETITIVE SYSTEM

In this paper, the impulsive exploitation of two species periodic competitive system is considered. First, we show that this type of system with impulsive harvesting has a unique positive periodicsolution, which is globally asymptotically stable. Further, by choosing the maximum total revenues as the management objective, we investigate the optimal harvesting policies for periodic competitive system with impulsive harvesting. Finally, we obtain the optimal time to harvest and optimal population level.

The theorem of the carrying simplex for competitive system defined on the n-rectangle and its application to a three-dimensional system

First, we show that the theorem by Hirsch which guarantees the existence of carrying simplex for competitive system on any n-rectangle： {x ∈ R^n ： 0 ≤ xi ≤ ki, i = 1,..., n} still holds. Next, based on the theorem a competitive system with the linear structure saturation defined on the n-rectangle is investigated, which admits a unique （n - 1）- dimensional carrying simplex as a global attractor. Further, we focus on the whole dynamical behavior of the three-dimensional case, which has a unique locally asymptotically stable positive equilibrium. Hopf bifurcations do not occur. We prove that any limit set is either this positive equilibrium or a limit cycle. If limit cycles exist, the number of them is finite. We also give a criterion for the positive equilibrium to be globally asymptotically stable.

THE DYNAMICAL BEHAVIOR ON THE CARRYING SIMPLEX OF A THREE-DIMENSIONAL COMPETITIVE SYSTEM： II. HYPERBOLIC STRUCTURE SATURATION

A competitive system on the n-rectangle： {x ∈ Rn： 0 ≤ xi ≤ li, i = 1,... ,n} was con- sidered, each species of which, in isolation, admits logistic growth with the hyperbolic structure saturation. It has an （n - 1）-dimensional invariant surface called carrying simplex E as a globe attractor, hence the long term dynamics of the system is com- pletely determined by the dynamics on E. For the three-dimensional system, the whole dynamical behavior was presented. It has a unique positive equilibrium point and any limit set is either an equilibrium point or a limit cycle. The system is permanent and it is proved that the number of periodic orbits is finite and non-periodic oscillation the May Leonard phenomenon does not exist. A criterion for the positive equilibrium to be globally asymptotically stable is provided. Whether there exist limit cycles or not remains open.

Single and competitive adsorption affinity of heavy metals toward peanut shell-derived biochar and its mechanisms in aqueous systems

Converting peanut shells into biochar by pyrolysis was considered an environmentally friendly and efficient method for agricultural solid waste disposal.The properties of peanut shell-derived biochar(PBC)under different temperature and its adsorption capacity of heavy metals were investigated.It was found that PBC400 exhibited the highest cumulative capability for heavy metals elimination in single solute because of its high specific surface area and rich functional groups.Furthermore,the competitive adsorption revealed that PBC had a substantial difference in adsorption affinity from diverse heavy metal ions,sorption capacity decreased as Pb2+>Cu2+>Cd2+>Ni2+>Zn2+,which was lower than in a single solute.The adsorption process using selected biochar was optimized with respect to p H,reaction time,adsorbent dose,and initial concentration of heavy metals.The kinetic data was well fitted with PSO model,and the Langmuir model was adopted for adsorption equilibrium data in both cases of single solutes and mixed solutes for all heavy metals,which indicated that the removal course was primarily explained by monolayer adsorption,and chemical adsorption occupied an important role.Therefore,peanut shells derived biochar could be a potential and green adsorbent for wastewater treatment.

Incorporating two coupling noises into a nonlinear competitive system with saturation effect

In this paper,a novel stochastic two-species competitive system with saturation effect is formulated,in which there exist two noise resources and their coupling mode is relatively complex and every noise source has elfect on the intrinsic growth rates of both species.With the help of some suitable Lyapunov functions,sufficient conditions for stochastic permanence are established as exponential extinction,extinction,permanence in time average and asymptotic pathwise estimation of system.The effect of coupling noise on the asymptotic behaviors of the populations is shown.

ASYMPTOTIC PROPERTY FOR A LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH DELAYS AND DISPERSION

An n-species nonautonomous Lotka-Volterra competition and diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and by using the skill of constructing an appropriate Lyapunov function, the new sufficient conditions are obtained for the global asymptotic stability and the uniqueness of the positive periodic solution,