# 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} }

#### 231 Citations

PERIODICITY IN A DELAYED RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH EXPLOITED TERM

- Mathematics
- 2007

With the help of the coincidence degree and the related continu- ation theorem, we explore the existence of at least two periodic solutions of a delayed ratio-dependent predator-prey system with… Expand

A bioeconomic model of a ratio-dependent predator-prey system and optimal harvesting

- Mathematics
- 2006

This paper deals with the problem of a ratio-dependent prey-predator model with combined harvesting. The existence of steady states and their stability are studied using eigenvalue analysis.… Expand

Periodicity in a ratio-dependent predator-prey system with stage structure for predator

- Mathematics
- 2005

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a… Expand

Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time delay

- Mathematics
- 2002

Abstract A two-species ratio-dependent predator–prey model with distributed time delay is investigated. It is shown that the system is persistent under some appropriate conditions, and sufficient… Expand

Bifurcation Analysis in a Class of Delayed Predator-Prey Models

- Computer Science
- 2018 10th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC)
- 2018

A class of three-dimensional Gause-type predatorprey model with delay is considered. Firstly, the existence of Hopf bifurcation are obtained via employing the polynomial theorem by analyzing the… Expand

Stability and Hopf Bifurcation Analysis in a Delayed Gause-type Predator-prey Models

- Mathematics
- 2018

A class of delayed ratio-dependent Gause-type predator-prey model is considered. Firstly, the eigenvalue problem is studyed for the linearized system at the coexisting equilibrium and a group of… Expand

Global analysis in delayed ratio-dependent gause-type predator-prey models

- Mathematics
- 2017

A class of three-dimensional delayed Gause-type predator-prey model with ratio-dependent is considered. Firstly, we present some results, including the boundedness of solutions and the permanence of… Expand

GLOBAL ASYMPTOTIC STABILITY OF A DELAYED PREDATOR-PREY MODEL WITH HASSELL-VARLEY TYPE FUNCTIONAL

- 2012

Here, a predator-prey model with Hassell-Varley type functional responses is studied. Some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using… Expand

Global Stability Analysis of Predator-Prey Model with Harvesting and Delay

- Mathematics
- 2012

We study the global stability of a Michaelis-Menten type predator-prey model with harvesting and delay. Sufficient conditions on the system parameters are derived which guarantee that the equilibrium… Expand

Positive periodic solutions for the neutral ratio-dependent predator-prey model

- Computer Science, Mathematics
- Comput. Math. Appl.
- 2011

By using a continuation theorem based on coincidence degree theory, we obtain some new sufficient conditions for the existence of positive periodic solutions for the neutral ratio-dependent… Expand

#### References

SHOWING 1-10 OF 26 REFERENCES

Convergence Results in a Well-Known Delayed Predator-Prey System

- Mathematics
- 1996

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 type… Expand

Global Stability for a Class of Predator-Prey Systems

- Mathematics, Computer Science
- SIAM J. Appl. Math.
- 1995

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

- Mathematics
- 1995

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 negative… Expand

QUALITATIVE PROPERTIES OF CHEMOSTAT EQUATIONS WITH TIME DELAYS

- Mathematics
- 1995

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

- Mathematics
- 1993

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 if… Expand

Convergence in Lotka–Volterra-type delay systems without instantaneous feedbacks

- Geography
- 1993

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 a… Expand

Empirical Evidence of the Role of Heterogeneity in Ratio‐Dependent Consumption

- Biology
- 1993

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

- Biology
- 1992

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

- Biology
- 1992

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

- Biology
- 1991

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