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Applied Mathematics and Computation, ISSN 0096-3003, 12/2017, Volume 314, pp. 193 - 198
A constant prey refuge has been incorporated in a stage structured predator–prey model with ratio-dependent functional response. Sufficient conditions are... 
Ratio dependent | Stage structure | Prey refuge | SYSTEM | MATHEMATICS, APPLIED | BEHAVIOR | DYNAMICS | Analysis | Models | Numerical analysis
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2011, Volume 235, Issue 5, pp. 1326 - 1341
A stochastic ratio-dependent predatorprey model is investigated in this paper. By the comparison theorem of stochastic equations and It's formula, we obtain... 
It's formula | Stable in time average | Extinction | Persistent in mean | Stochastic ratio-dependent predatorprey system
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 02/2020, Volume 51, p. 102962
The ratio-dependent predator–prey model exhibits rich dynamics due to the singularity of the origin. Harvesting in a ratio-dependent predator–prey model is... 
Pattern formation | Turing instability | Predator–prey model | Harvesting rate | Ratio-dependent
Journal Article
Journal of Physics D: Applied Physics, ISSN 0022-3727, 07/2014, Volume 47, Issue 27, p. 273001
Plasma etching has been enabling nano-electronic fabrication since the 1980s; during this time, transistor size has shrunk by nearly two orders of magnitude,... 
aspect ratio-dependent etch | precision etch | grand etch challenges | line width roughness | atomic layer etch | PHYSICS, APPLIED | ASPECT RATIO
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 05/2019, Volume 521, pp. 614 - 625
In this paper, we study the dynamical behavior of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate. We propose a stochastic... 
Ratio-dependent incidence rate | Stationary distribution and ergodicity | Extinction | Markov switching | Threshold | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | STATIONARY DISTRIBUTION | DYNAMICS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2018, Volume 264, Issue 5, pp. 3559 - 3595
This paper deals with a ratio-dependent predator–prey system with the crowing term and the weak growth in the prey equation. Under the condition that the... 
Persistence | Stability | Crowding effect | Ratio-dependent predator–prey system | Multiple positive solutions | Computer science
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 09/2019
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 07/2019, Volume 526, p. 120803
Stochastic predator–prey systems with different functional responses have been studied. But the dynamics of a Michaelis–Menten-type ratio-dependent... 
Ergodicity | Extinction | Stochastic ratio-dependent predator–prey system | Non-persistence | Stationary distribution | HETEROCLINIC BIFURCATION | QUALITATIVE-ANALYSIS | PHYSICS, MULTIDISCIPLINARY | MODEL | Stochastic ratio-dependent predator-prey system
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 496 - 508
In this paper, a delayed ratio-dependent predator–prey model with Holling type III functional response and stage structure for the predator is considered. By... 
Predator–prey system | Hopf bifurcation | Local stability | Ratio-dependent | Predator-prey system | SYSTEM | MATHEMATICS, APPLIED | Analysis | Models | Numerical analysis
Journal Article
Journal Article
Journal of Micromechanics and Microengineering, ISSN 0960-1317, 09/2018, Volume 28, Issue 11, p. 117001
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2018, Volume 460, Issue 1, pp. 458 - 475
A ratio-dependent Holling–Tanner predator–prey model is studied. By investigating the local stability properties of equilibrium points and periodic solutions... 
Existence and nonexistence of periodic solution | Poincaré–Bendixson Theorem | Global dynamics | Ratio-dependent | periodic solution | MATHEMATICS | MATHEMATICS, APPLIED | Existence and nonexistence of | STABILITY | Poincare-Bendixson Theorem | MODEL
Journal Article
Science of the Total Environment, ISSN 0048-9697, 04/2019, Volume 662, pp. 307 - 312
Harmful cyanobacterial blooms have caused serious threat to the sustainable development of freshwater ecosystems due to eutrophication, but there is no... 
Phosphorus | Harmful algal blooms | Ecological nutrient thresholds | Ratio-dependent model | Nitrogen | Eutrophication | EUTROPHIC LAKE TAIHU | IDENTIFICATION | DENSITY | ENVIRONMENTAL SCIENCES | MODELS | MAINTENANCE ENERGY | PHYTOPLANKTON | Chlorophyll | Growth | Analysis | Water pollution | Ecological restoration | Sustainable development | Index Medicus
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2015, Volume 428, Issue 2, pp. 817 - 837
In this paper, a Filippov ratio-dependent predator–prey model is proposed to describe the effect on behavioral refuges caused by prey instinct anti-predator... 
Refuge | Filippov system | Finite time stable | Ratio-dependent | MATHEMATICS | MATHEMATICS, APPLIED | GLOBAL QUALITATIVE-ANALYSIS | DYNAMICS | FINITE-TIME STABILITY
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 09/2015, Volume 20, Issue 7, pp. 2269 - 2290
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 09/2016, Volume 72, Issue 6, pp. 1727 - 1742
This paper is concerned with the -species predator–prey models in a bounded domain in two cases, one of which involves cooperative preys and the other involves... 
Degenerate diffusion | Dynamical behavior | Stability | Ratio-dependent reaction | Predator–prey models | Global attractor | Models | Numerical analysis | Specific gravity | Analysis
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 2011, Volume 12, Issue 4, pp. 2319 - 2338
In this paper, we show that under suitable simple assumptions the classical two populations system may exhibit unexpected behaviors. Considering a more... 
Predator–prey | Bifurcations | Limit cycles | Group defense | Predatorprey | MATHEMATICS, APPLIED | PREY | Predator-prey | STABILITY | RATIO-DEPENDENT PREDATION | Competition | Symbiosis | Nonlinearity | Mathematical models | Thresholds | Hopf bifurcation
Journal Article
Ecological Modelling, ISSN 0304-3800, 02/2013, Volume 250, pp. 134 - 142
► MSY level always depends on the intra-specific competition rate of predator. ► MSY level of prey species makes a ratio dependent prey predator system... 
Persistence | Intraspecific competition | Prey–predator | Maximum sustainable total yield | Ratio-dependent | Prey-predator | MODELS | COMPETITION | ECOLOGY | Wildlife conservation
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 02/2019, Volume 389, pp. 51 - 63
A novel Michaelis–Menten type ratio-dependent predator–prey model with predator-age structure is investigated. The predator fertility function is considered to... 
Michaelis–Menten type | Non-densely defined Cauchy problem | Hopf bifurcation | Predator-prey model | Age structure | Ratio-dependent | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | STABILITY | PHYSICS, MATHEMATICAL | DYNAMICS | INFECTION | Michaelis-Menten type | BIFURCATION | Analysis | Models | Numerical analysis
Journal Article
International Journal of Multimedia and Ubiquitous Engineering, ISSN 1975-0080, 2015, Volume 10, Issue 2, pp. 111 - 120
Journal Article
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