Bifurcations of a predator-prey system with weak allee effects
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National Natural Science Foundation of China [10601042]; Fundamental Research Funds the Central Universities [HIT.NSRIF.2010052]Abstract:
National Natural Science Foundation of China [10601042]; Fundamental Research Funds the Central Universities [HIT.NSRIF.2010052]read more
Citations
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Differential Equations and Dynamical Systems
TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
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An SEI infection model incorporating media impact
TL;DR: A susceptible-exposed-infective (SEI) model, including individuals' behavior changes in their contacts due to the influences of media coverage, is used, and it is shown that given larger ?
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Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay
TL;DR: In this article, the existence, boundedness, and stability of the equilibria of a predator-prey model with weak Allee effect were qualitatively discussed. And the results showed that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values.
Journal ArticleDOI
A Simple Predator-Prey Population Model with Rich Dynamics
TL;DR: In this article, a non-smooth switched harvest on predators is introduced into a simple predator-prey model with logistical growth of the prey and a bilinear functional response, and it is shown that the system is permanent and there may exist multiple positive equilibria due to the effects of the switched harvest, a saddle-node bifurcation, a limit cycle, and the coexistence of a stable equilibrium and a unstable circled inside limit cycle and a stable circled outside limit cycle.
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Multiple limit cycles in a Leslie–Gower-type predator–prey model considering weak Allee effect on prey
TL;DR: In this article, a modified Leslie-Gower-type predator-prey model is analyzed, considering now that the prey population is affected by a weak Allee effect, complementing results obtained in previous papers in which the consequences of strong allee effect for the same model were established.
References
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Book
Differential Equations and Dynamical Systems
TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
Book
Elements of Physical Biology
TL;DR: The author has the problem of evolution always before him, and considers analytically the effect on population of a change in the behaviour of individuals in Elements of Physical Biology.
Journal ArticleDOI
What Is the Allee Effect
TL;DR: This work proposes a definition for the Allee effect and attempts to resolve the major issues underlying the confusion surrounding this term.
Journal ArticleDOI
Fluctuations in the Abundance of a Species considered Mathematically
TL;DR: In this paper, Lotka observed that he had obtained the differential equations in the case of two species, one of which feeds upon the other, and that he gave, as well as myself, the same diagram of the integral, and also the period in the cases of small fluctuations.