Stability analysis of a single neuron model with delay

AbstractIn this paper we study the asymptotic behavior and numerical approximation of the single neuron model equation ẋ(t)=−dx(t)+af(x(t))+bf(x(t−τ))+I, t⩾0 (1), where d>0 and f(x)=0.5(|x+1|−|x−1|). We obtain new sufficient conditions for global asymptotic stability of constant equilibriums of (1), give several numerical examples to illustrate our results, and formulate conjectures on the asymptotic behavior of the solutions based on our numerical experiments

Permanence in a class of delay differential equations with mixed monotonicity

In this paper we consider a class of delay differential equations of the form $\dot{x}(t)=\alpha (t) h(x(t-\tau), x(t-\sigma))-\beta(t)f(x(t))$, where $h$ is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit superior of the solutions via a special solution of an associated nonlinear system of algebraic equations. The results are generated to a more general class of delay differential equations with mixed monotonicity

Differenciál- és differenciaegyenletek kvalitatív és kvantitatív elmélete alkalmazásokkal = Qualitative and quantitative theory of differential and difference equations with applications

Kutatásaink a következő témakörökhöz kapcsolódtak: Megoldások aszimptotikus jellemzése és stabilitása; integrálegyenletek és egyenlőtlenségek mértékterekben; differenciálegyenletek megoldásainak paraméterektől való differenciálható függése, paraméterek becslése; állapotfüggő késleltetésű differenciálegyenletek stabilitása. A 2004-2007 kutatási időszakban 31 publikációnk jelent meg. Dolgoztainkra az elmúlt négy évben 575, ezen belül a kutatási periódusban megjelent 31 publikációnkra pedig 57 hivatkozást regisztráltunk. Eredményeinkről 9 plenáris, 33 meghívott szekció és 16 szekció előadásban számoltunk be nemzetközi konferenciákon. Ezeken kívül 34 meghívott előadást tartottunk különböző hazai és külföldi egyetemek szakmai szemináriumain. | Our research is related to the following topics: Asymptotic characterization and stability of solutions; integral equations and inequalities in measure spaces; differentiability of the solutions with respect to the parameters, and parameter estimation methods; stability of differential equations with state-dependent delays. 31 of our pubications have appeared in the research period 2004-2007. We have counted 575 citations of our papers in the last four years, including 57 citations of our 31 papers published in this period. We gave 9 plenary, 33 invited, and 16 contributed talks at international conferences, and 34 invited talks at research seminars of national and foreign universities

Permanence in a class of delay differential equations with mixed monotonicity

In this paper we consider a class of delay differential equations of the form x˙(t) = α(t)h(x(t − τ), x(t − σ)) − β(t)f(x(t)), where h is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit superior of the solutions via a special solution of an associated nonlinear system of algebraic equations. The results are generated to a more general class of delay differential equations with mixed monotonicity

Permanence in a class of delay differential equations with mixed monotonicity

In this paper we consider a class of delay differential equations of the form x˙(t) = α(t)h(x(t − τ), x(t − σ)) − β(t)f(x(t)), where h is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit superior of the solutions via a special solution of an associated nonlinear system of algebraic equations. The results are generated to a more general class of delay differential equations with mixed monotonicity

Recurrent acute pancreatitis prevention by the elimination of alcohol and cigarette smoking (REAPPEAR): protocol of a randomised controlled trial and a cohort study

Background/objectives Acute recurrent pancreatitis (ARP) due to alcohol and/or tobacco abuse is a preventable disease which lowers quality of life and can lead to chronic pancreatitis. The REAPPEAR study aims to investigate whether a combined patient education and cessation programme for smoking and alcohol prevents ARP. Methods and analysis The REAPPEAR study consists of an international multicentre randomised controlled trial (REAPPEAR-T) testing the efficacy of a cessation programme on alcohol and smoking and a prospective cohort study (REAPPEAR-C) assessing the effects of change in alcohol consumption and smoking (irrespective of intervention). Daily smoker patients hospitalised with alcohol-induced acute pancreatitis (AP) will be enrolled. All patients will receive a standard intervention priorly to encourage alcohol and smoking cessation. Participants will be subjected to laboratory testing, measurement of blood pressure and body mass index and will provide blood, hair and urine samples for later biomarker analysis. Addiction, motivation to change, socioeconomic status and quality of life will be evaluated with questionnaires. In the trial, patients will be randomised either to the cessation programme with 3-monthly visits or to the control group with annual visits. Participants of the cessation programme will receive a brief intervention at every visit with direct feedback on their alcohol consumption based on laboratory results. The primary endpoint will be the composite of 2-year all-cause recurrence rate of AP and/or 2-year all-cause mortality. The cost-effectiveness of the cessation programme will be evaluated. An estimated 182 participants will be enrolled per group to the REAPPEAR-T with further enrolment to the cohort