October  2010, 14(3): 1095-1103. doi: 10.3934/dcdsb.2010.14.1095

Global properties of a general predator-prey model with non-symmetric attack and consumption rate


MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick

Received  October 2009 Revised  December 2009 Published  July 2010

Identification of conditions for stable coexistence of interacting populations is a problem of the highest priority in mathematical biology. This problem is usually considered under specific assumptions made regarding the functional forms of non-linear feedbacks. Apparently, such an approach is lacking generality. In this paper, we consider the dynamics of two species with interaction of predator--prey (consumer-supplier) type with the assumption that a part of the resource is neglected or wasted by the predator (consumer). This model describes, for instance, killing for fun; such behaviour is typical for many predators when the prey is abundant.
   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.
Citation: Andrei Korobeinikov. Global properties of a general predator-prey model with non-symmetric attack and consumption rate. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1095-1103. doi: 10.3934/dcdsb.2010.14.1095

Shuhua Zhang, Longzhou Cao, Zuliang Lu. An EOQ inventory model for deteriorating items with controllable deterioration rate under stock-dependent demand rate and non-linear holding cost. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021156


Hamza Khalfi, Amal Aarab, Nour Eddine Alaa. Energetics and coarsening analysis of a simplified non-linear surface growth model. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021014


Yunfei Lv, Yongzhen Pei, Rong Yuan. On a non-linear size-structured population model. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 3111-3133. doi: 10.3934/dcdsb.2020053


Michael Y. Li, Xihui Lin, Hao Wang. Global Hopf branches and multiple limit cycles in a delayed Lotka-Volterra predator-prey model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 747-760. doi: 10.3934/dcdsb.2014.19.747


Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2997-3022. doi: 10.3934/dcdsb.2020217


Kousuke Kuto, Yoshio Yamada. Coexistence states for a prey-predator model with cross-diffusion. Conference Publications, 2005, 2005 (Special) : 536-545. doi: 10.3934/proc.2005.2005.536


Paolo Buttà, Franco Flandoli, Michela Ottobre, Boguslaw Zegarlinski. A non-linear kinetic model of self-propelled particles with multiple equilibria. Kinetic & Related Models, 2019, 12 (4) : 791-827. doi: 10.3934/krm.2019031


Francesca Biagini, Katharina Oberpriller. Reduced-form setting under model uncertainty with non-linear affine intensities. Probability, Uncertainty and Quantitative Risk, 2021, 6 (3) : 159-188. doi: 10.3934/puqr.2021008


Rui Xu, M.A.J. Chaplain, F.A. Davidson. Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 823-831. doi: 10.3934/dcdsb.2004.4.823


Cruz Vargas-De-León, Alberto d'Onofrio. Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1019-1033. doi: 10.3934/mbe.2017053


Anugu Sumith Reddy, Amit Apte. Stability of non-linear filter for deterministic dynamics. Foundations of Data Science, 2021, 3 (3) : 647-675. doi: 10.3934/fods.2021025


H. W. Broer, K. Saleh, V. Naudot, R. Roussarie. Dynamics of a predator-prey model with non-monotonic response function. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 221-251. doi: 10.3934/dcds.2007.18.221


Hiroshi Ito. Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 5171-5196. doi: 10.3934/dcdsb.2020338


Malay Banerjee, Nayana Mukherjee, Vitaly Volpert. Prey-predator model with nonlocal and global consumption in the prey dynamics. Discrete & Continuous Dynamical Systems - S, 2020, 13 (8) : 2109-2120. doi: 10.3934/dcdss.2020180


Faustino Sánchez-Garduño, Philip K. Maini, Judith Pérez-Velázquez. A non-linear degenerate equation for direct aggregation and traveling wave dynamics. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 455-487. doi: 10.3934/dcdsb.2010.13.455


Guirong Jiang, Qishao Lu. The dynamics of a Prey-Predator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1301-1320. doi: 10.3934/dcdsb.2006.6.1301


Li Ma, Shangjiang Guo. Bifurcation and stability of a two-species diffusive Lotka-Volterra model. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1205-1232. doi: 10.3934/cpaa.2020056


Yukio Kan-On. Global bifurcation structure of stationary solutions for a Lotka-Volterra competition model. Discrete & Continuous Dynamical Systems, 2002, 8 (1) : 147-162. doi: 10.3934/dcds.2002.8.147


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) : 2513-2531. doi: 10.3934/cpaa.2020110


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) : 381-400. doi: 10.3934/mbe.2015008

2020 Impact Factor: 1.327


  • PDF downloads (56)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]