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Relaxation Oscillations in Predator–Prey Systems
Journal of Dynamics and Differential Equations, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ai, Shangbing, Yi, Yingfei
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Phase transitions in predator-prey systems
Physical Review E, 2012The relationship between predator and prey plays an important role in ecosystem conservation. However, our understanding of the principles underlying the spatial distribution of predators and prey is still poor. Here we present a phase diagram of a predator-prey system and investigate the lattice formation in such a system.
Seido, Nagano, Yusuke, Maeda
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Coexistence in a predator-prey system
Physical Review E, 2001We propose a lattice model of two populations, predators and prey. The model is solved via Monte Carlo simulations. Each species moves randomly on the lattice and can live only a certain time without eating. The lattice cells are either grass (eaten by prey) or tree (giving cover for prey). Each animal has a reserve of food that is increased by eating (
M, Droz, A, Pekalski
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Epidemics spreading in predator–prey systems
International Journal of Computer Mathematics, 2012In this paper, we consider an ecosystem in which two disease-affected populations thrive and in which the epidemics can spread from one species to the other one by contact. The feasibility and stability conditions of the equilibria of the system are investigated analytically. The model does not possess Hopf bifurcations.
CHAUDHURI, Sanjay +2 more
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Weakly dissipative predator-prey systems
Bulletin of Mathematical Biology, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
King, A. A. +4 more
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Travelling Waves in Predator-Prey Systems
SIAM Journal on Mathematical Analysis, 1993Summary: The existence of travelling wave solutions to reaction-diffusion equations which model predator-prey systems is proven. Bistable waves, Fisher waves, and higher-dimensional analogues of Fisher waves are found. Some of the systems investigated have bistable homoclinic waves.
Mischaikow, Konstantin +1 more
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Wave propagation in predator–prey systems
Nonlinearity, 2015The authors study a class of predator-prey systems of reaction-diffusion type. The examples of such systems include Holling functional response systems, Ivlev type functional response systems, and the SIR model. In the context of these systems, the authors are interested in the dynamical behavior of solutions with the initial disturbances where the ...
Fu, Sheng-Chen, Tsai, Je-Chiang
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Periodic Time-Dependent Predator-Prey Systems
SIAM Journal on Applied Mathematics, 1977The general system of differential equations describing predator-prey dynamics is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifurcation theory, as well as a recent global result of Rabinowitz, it is shown that this system has a periodic solution (in place of an equilibrium ...
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A Predator–Prey system with anorexia response
Nonlinear Analysis: Real World Applications, 2007This paper treats a predator-prey model with one predator and two prey species. It is assumed that there is a saturation effect with respect to the first prey species, while the predator response to the second prey species is of anorexia type. All the coefficients that usually are regarded constant, now are allowed to be nonnegative almost periodic ...
Huang, Zhenkun +2 more
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Harvesting in discrete-time predator-prey systems
Mathematical Biosciences, 1997Fisheries for assemblages of interacting species with seasonal recruitment occur throughout temperate and boreal regions of the world ocean. Such systems are conveniently modeled within a difference-equation framework. Here, we examine the dynamic behavior of discrete-time models for an exploited predator-prey system. We contrast the dynamic properties
Basson, Marinelle, Fogarty, Michael J.
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