Global analyses in some delayed ratio-dependent predator-prey systems

@article{Beretta1998GlobalAI,
  title={Global analyses in some delayed ratio-dependent predator-prey systems},
  author={Edoardo Beretta and Yang Kuang},
  journal={Nonlinear Analysis-theory Methods \& Applications},
  year={1998},
  volume={32},
  pages={381-408}
}
  • E. Beretta, Y. Kuang
  • Published 1998
  • Mathematics
  • Nonlinear Analysis-theory Methods & Applications
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References

SHOWING 1-10 OF 26 REFERENCES
Convergence Results in a Well-Known Delayed Predator-Prey System
Abstract In this paper, we provide a detailed and explicit procedure of obtaining some regions of attraction for the positive steady state (assumed to exist) of a well known Lotka–Volterra typeExpand
Global Stability for a Class of Predator-Prey Systems
TLDR
The Dulac’s criterion is applied and Liapunov functions are constructed to establish the global stability of the positive locally asymptotically stable equilibrium in a class of predator-prey systems. Expand
Global Stability in Delay Differential Systems without Dominating Instantaneous Negative Feedbacks
Abstract Most of the global stability or convergence results appearing so far for delayed Lotka-Volterra-type systems or other delay differential systems require that the instantaneous negativeExpand
QUALITATIVE PROPERTIES OF CHEMOSTAT EQUATIONS WITH TIME DELAYS
The mathematical properties of chemostat equations with delayed growth and delayed nutrient recycling are summarized.
CONVERGENCE IN LOTKA-VOLTERRA TYPE DIFFUSIVE DELAY SYSTEMS WITHOUT DOMINATING INSTANTANEOUS NEGATIVE FEEDBACKS
This paper deals with the convergence aspect of diffusive delay Lotka-Volterra systems with infinite delays. It is well known that such a system has a globally asymptotically stable steady state ifExpand
Convergence in Lotka–Volterra-type delay systems without instantaneous feedbacks
Most of the convergence results appearing so far for delayed Lotka-Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such aExpand
Empirical Evidence of the Role of Heterogeneity in Ratio‐Dependent Consumption
TLDR
The design is such that the two types of dependence can be discriminated by observation of equilibrium patterns, and it is hypothesized that the applicability of one or the other model depends on the degree of heterogeneity of predators and prey in space, the prey- dependent model being appropriate in homogeneous situations while the ratio-dependent model is appropriate in heterogeneous situations. Expand
Consequences of Ratio‐Dependent Predation for Steady‐State Properties of Ecosystems
TLDR
The results show parallel increases in all trophic levels as a result of increased nutrient input, demonstrating that natural systems are closer to ratio dependence than to prey dependence. Expand
The Orgins and Evolution of Predator‐Prey Theory
TLDR
Predator-prey models that evolved from logistic theory or that incor- porate ratio-dependent functional responses do not have these problems and also seem to be more biologically plausible. Expand
Functional responses and heterogeneities: an experimental test with cladocerans
TLDR
Experiments using four filter-feeding cladoceran species were designed to test the hypothesis that species with homogeneous spatial behaviour follow prey- dependent dynamics while those with heterogeneous behaviour follow ratio-dependent dynamics and to investigate the relation between individual behaviour and population dynamics. Expand
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