
Previous Article
Stationary patterns for an adsorbateinduced phase transition model I: Existence
 DCDSB Home
 This Issue

Next Article
Analysis of a predatorprey model with predators impulsively diffusing between two patches
Global properties of a general predatorprey model with nonsymmetric attack and consumption rate
1.  MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick 
We assume that the functional responses that are usually included in such models are given by unspecified functions. Using the direct Lyapunov method, we derive the conditions which ensure global asymptotic stability of this model. It is remarkable that these conditions impose much weaker constraints on the system properties than that are usually assumed.
[1] 
Hamza Khalfi, Amal Aarab, Nour Eddine Alaa. Energetics and coarsening analysis of a simplified nonlinear surface growth model. Discrete & Continuous Dynamical Systems  S, 2021 doi: 10.3934/dcdss.2021014 
[2] 
Yunfei Lv, Yongzhen Pei, Rong Yuan. On a nonlinear sizestructured population model. Discrete & Continuous Dynamical Systems  B, 2020, 25 (8) : 31113133. doi: 10.3934/dcdsb.2020053 
[3] 
Michael Y. Li, Xihui Lin, Hao Wang. Global Hopf branches and multiple limit cycles in a delayed LotkaVolterra predatorprey model. Discrete & Continuous Dynamical Systems  B, 2014, 19 (3) : 747760. doi: 10.3934/dcdsb.2014.19.747 
[4] 
Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reactiondiffusionadvection SIS epidemic model with saturated incidence rate. Discrete & Continuous Dynamical Systems  B, 2021, 26 (6) : 29973022. doi: 10.3934/dcdsb.2020217 
[5] 
Kousuke Kuto, Yoshio Yamada. Coexistence states for a preypredator model with crossdiffusion. Conference Publications, 2005, 2005 (Special) : 536545. doi: 10.3934/proc.2005.2005.536 
[6] 
Paolo Buttà, Franco Flandoli, Michela Ottobre, Boguslaw Zegarlinski. A nonlinear kinetic model of selfpropelled particles with multiple equilibria. Kinetic & Related Models, 2019, 12 (4) : 791827. doi: 10.3934/krm.2019031 
[7] 
Rui Xu, M.A.J. Chaplain, F.A. Davidson. Periodic solutions of a discrete nonautonomous LotkaVolterra predatorprey model with time delays. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 823831. doi: 10.3934/dcdsb.2004.4.823 
[8] 
Cruz VargasDeLeón, Alberto d'Onofrio. Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences & Engineering, 2017, 14 (4) : 10191033. doi: 10.3934/mbe.2017053 
[9] 
H. W. Broer, K. Saleh, V. Naudot, R. Roussarie. Dynamics of a predatorprey model with nonmonotonic response function. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 221251. doi: 10.3934/dcds.2007.18.221 
[10] 
Malay Banerjee, Nayana Mukherjee, Vitaly Volpert. Preypredator model with nonlocal and global consumption in the prey dynamics. Discrete & Continuous Dynamical Systems  S, 2020, 13 (8) : 21092120. doi: 10.3934/dcdss.2020180 
[11] 
Faustino SánchezGarduño, Philip K. Maini, Judith PérezVelázquez. A nonlinear degenerate equation for direct aggregation and traveling wave dynamics. Discrete & Continuous Dynamical Systems  B, 2010, 13 (2) : 455487. doi: 10.3934/dcdsb.2010.13.455 
[12] 
Hiroshi Ito. Inputtostate stability and Lyapunov functions with explicit domains for SIR model of infectious diseases. Discrete & Continuous Dynamical Systems  B, 2021, 26 (9) : 51715196. doi: 10.3934/dcdsb.2020338 
[13] 
Guirong Jiang, Qishao Lu. The dynamics of a PreyPredator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems  B, 2006, 6 (6) : 13011320. doi: 10.3934/dcdsb.2006.6.1301 
[14] 
Tomás Caraballo, Mohamed El Fatini, Idriss Sekkak, Regragui Taki, Aziz Laaribi. A stochastic threshold for an epidemic model with isolation and a non linear incidence. Communications on Pure & Applied Analysis, 2020, 19 (5) : 25132531. doi: 10.3934/cpaa.2020110 
[15] 
Li Ma, Shangjiang Guo. Bifurcation and stability of a twospecies diffusive LotkaVolterra model. Communications on Pure & Applied Analysis, 2020, 19 (3) : 12051232. doi: 10.3934/cpaa.2020056 
[16] 
Yukio KanOn. Global bifurcation structure of stationary solutions for a LotkaVolterra competition model. Discrete & Continuous Dynamical Systems, 2002, 8 (1) : 147162. doi: 10.3934/dcds.2002.8.147 
[17] 
Xiao He, Sining Zheng. Protection zone in a modified LotkaVolterra model. Discrete & Continuous Dynamical Systems  B, 2015, 20 (7) : 20272038. doi: 10.3934/dcdsb.2015.20.2027 
[18] 
C. Connell McCluskey. Global stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 381400. doi: 10.3934/mbe.2015008 
[19] 
Hong Yang, Junjie Wei. Global behaviour of a delayed viral kinetic model with general incidence rate. Discrete & Continuous Dynamical Systems  B, 2015, 20 (5) : 15731582. doi: 10.3934/dcdsb.2015.20.1573 
[20] 
Shouying Huang, Jifa Jiang. Global stability of a networkbased SIS epidemic model with a general nonlinear incidence rate. Mathematical Biosciences & Engineering, 2016, 13 (4) : 723739. doi: 10.3934/mbe.2016016 
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]