Hopf bifurcation in three-species food chain models with group defense
References (40)
- et al.
Discrete delay, distributed delay and stability switches
J. Math. Anal. Appl.
(1982) - et al.
Three species food chain models with mutual interference and time delays
Math. Biosci.
(1986) - et al.
Interactions leading to persistence in predator-prey systems with group defense
Bull. Math. Biol.
(1988) - et al.
The trade-off between mutual interference and time lags in predator-prey systems
Bull. Math. Biol.
(1983) - et al.
Global stability and persistence of simple food chains
Math. Biosci.
(1985) - et al.
Predator-prey systems with group defense: the paradox of enrichment revised
Bull. Math. Biol.
(1986) Some global results for nonlinear eigenvalue problems
J. Functional Anal.
(1971)- et al.
Persistence in three-species food chain models with group defense
Math. Biosci.
(1991) - et al.
Homage to the red queen. Part I. Coevolution of predators and their victims
Theoret. Pop. Biol.
(1978) - et al.
Dynamics of a chemostat culture: the effect of a delay in a cell response
J. Theor. Biol.
(1974)
Kinetics of intrite oxydation
Nitrobacter Winogrodski Biochem. J.
Methods of Bifurcation
On zeros of some transcendental equations
Funkcial. Ekvac.
Integrodifferential Equations and Delay Models in Population Dynamics
Deterministic Mathematical Models in Population Ecology
Nonoccurrence of stability switching in systems with discrete delays
Canad. Math. Bull.
Stability criteria for a system involving two time delays
SIAM J. Appl. Math.
Enriched predator-prey systems: theoretical stability
Science
Delayed responses and stability in two-species systems
J. Austral. Math. Soc. Ser. B
Limit cycles in two-species competition with time delays
J. Austral. Math. Soc. Ser. B
Cited by (65)
Dynamics of a two-prey one-predator model with fear and group defense: A study in parameter planes
2024, Chaos, Solitons and FractalsCanard phenomena for a slow-fast predator-prey system with group defense of the prey
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2019, Applied Mathematics and ComputationCitation Excerpt :There are many good examples in population ecology which have verified the phenomenon of group defense: Lone musk ox can be successfully attacked by wolves [3]; Large swarms of insects are able to hide, making it difficult for their predators to identify them [4]. Group defense has become an important focus of research and analyzed mathematically in detail (see references [5–15]). When considering the pest-natural enemy ecosystem, it is necessary to take into account Integrated Pest Management (IPM) strategies [17–22] in order to prevent agricultural or ecological damage from pest disaster outbreaks, which involves choosing appropriate measures from a range of pest control techniques including biological, cultural and chemical methods to suit individual cropping systems, pest complexes and local environments.
Impact of Fear and Group Defense on the Dynamics of a Predator-Prey System
2024, International Journal of Bifurcation and Chaos
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Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A 4823.
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Research partially supported by a University of Alberta Ph.D. Scholarship.